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The analysis of dielectric response function obtained from the power transformer is a well-accepted technique in insulation diagnosis. A convenient way of analysing time-domain dielectric response φ(t) is the formulation of simple resistance−capacitance-based circuits like the conventional Debye model (CDM) or the modified Debye model (MDM) that are capable of modelling φ(t). However, available techniques do not guarantee unique branch parameters of such circuits for a given φ(t). In fact, the branch parameters are known to depend on the curve-fitting procedure opted during model formulation. This makes accuracy of CDM and MDM parameter-based diagnosis techniques less reliable. Furthermore, it seems logical to analyse the time-domain dielectric response of oil-paper insulation using a model containing time-varying parameters. In this study, a methodology is proposed using which such an insulation model (containing time-varying parameters) is formulated using time-domain insulation response. Related analysis presented suggests that the proposed model is immune to problems associated with available insulation models (containing time-invariant parameters). The performance of the proposed model in indicating insulation condition is tested on data obtained from several real-life power transformers.

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.

We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval $$T$$ . Taking $$T$$ as a bifurcation parameter, we demonstrate the existence of (non-degenerate) Hopf bifurcations in these systems and present an analysis of the resulting limit cycles using Lindstedt’s method.

A generalized approach to design a proportional and derivative system faults fuzzy observer for continuous-time nonlinear systems described in the Takagi-Sugeno descriptor statespace form is presented in the paper. Considering measurable premise variables, the problem addressed is formulated as an enhanced concept to descriptor systems design, implying the asymptotic convergence both the state observer error as fault estimate error. Presented in the sense of the second Lyapunov method, an associated structure of linear matrix inequalities is outlined to possess the global observer asymptotic dynamic properties with compiling the local insiders by inference through the membership functions equal those of the system model. The proposed design conditions are verified by simulations in the numerical illustrative example.

In this work, important aspects of bacteriocin producing bacteria and their interplay are elucidated. Various attempts to model the resistant, producer and sensitive Escherichia coli strains in the so-called rock-scissors-paper (RSP) game had been made in the literature. The question arose whether there is a continuous model with a cyclic structure and admitting an oscillatory dynamics as observed in various experiments. The May-Leonard system admits a Hopf bifurcation, which is, however, degenerate and hence inadequate. The traditional differential equation model of the RSP-game cannot be applied either to the bacteriocin system because it involves positive interaction terms. In this paper, a plausible competitive Lotka-Volterra system model of the RSP game is presented and the dynamics generated by that model is analyzed. For the first time, a continuous, spatially homogeneous model that describes the competitive interaction between bacteriocin-producing, resistant and sensitive bacteria is established. The interaction terms have negative coefficients. In some experiments, for example, in mice cultures, migration seemed to be essential for the reinfection in the RSP cycle. Often statistical and spatial effects such as migration and mutation are regarded to be essential for periodicity. Our model gives rise to oscillatory dynamics in the RSP game without such effects. Here, a normal form description of the limit cycle and conditions for its stability are derived. The toxicity of the bacteriocin is used as a bifurcation parameter. Exact parameter ranges are obtained for which a stable (robust) limit cycle and a stable heteroclinic cycle exist in the three-species game. These parameters are in good accordance with the observed relations for the E. coli strains. The roles of growth rate and growth yield of the three strains are discussed. Numerical calculations show that the sensitive, which might be regarded as the weakest, can have the longest sojourn times.

This paper deals with the exponential stabilizability of the class of stochastic systems with jumps. For the case of linear uncertain stochastic system, we have designed an optimal control law that guarantees the exponential stability robustness of systems with Markovian jumps. For the nonlinear case with matching conditions, we have established a similar result.

The research in this paper focuses on a state estimation problem for paper path and heat flow control of industrial printers. The nonlinear dynamics can be approximated, up to an arbitrary accuracy, with a piecewise linear system, and an arbitrary time driven switching law. The stability and performance of the estimators are analyzed and proven based on Lyapunov theory. Simulation examples show the effectiveness of the proposed approaches in the presence of several switches between modes.

We present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed-loop stability. The scheme can be applied to both stable and unstable systems with input constraints. The objective functional to be minimized consists of an integral square error (ISE) part over a finite time horizon plus a quadratic terminal cost. The terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate Lyapunov equation. Furthermore, the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region. If the Jacobian linearization of the nonlinear system to be controlled is stabilizable, we prove that feasibility of the open-loop optimal control problem at time t=0 implies asymptotic stability of the closed-loop system. The size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense.

This paper is concerned with robust stabilization for linear and bilinear systems with nonlinear uncertainty. By using quadratic Lyapunov functions, our controls guarantee the uniform exponential stability of uncertain systems. Moreover, the controls have a simple structure and are easily handled. Some problems of H∞ control for these systems are also considered. © 1997 Elsevier Science Ltd.

In a paper by Lee and Hedrick (1995), some conditions for the global asymptotic stability of linear systems under saturating controls were presented as new. We show that most of the results of this paper are already well-known and published. Therefore they cannot be considered as new.

This paper presents a fundamental spatial performance limitation analysis method for multiple array paper machine cross-directional (CD) processes based on a two-dimensional (temporal and spatial) frequency decomposition method. Paper machine CD processes are spatially-distributed dynamical systems. Due to their (almost) spatially invariant characteristic, the models of these systems are considered as transfer matrices with rectangular circulant matrix blocks, whose input and output singular vectors are the Fourier components of dimension equivalent to number of actuators and measurements respectively. Through this method, a fundamental spatial performance limitation of multiple array CD processes can be observed. A real industrial multiple array CD process is used for illustrating the effectiveness of this method.

Stability is essential for designing and controlling any dynamic systems. Recently, the stability of genetic regulatory networks has been widely studied by employing linear matrix inequality (LMI) approach, which results in checking the existence of feasible solutions to high-dimensional LMIs. In the previous study, the authors present several stability conditions for genetic regulatory networks with time-varying delays, based on M -matrix theory and using the non-smooth Lyapunov function, which results in determining whether a low-dimensional matrix is a non-singular M -matrix. However, the previous approach cannot be applied to analyse the stability of genetic regulatory networks with noise perturbations. Here, the authors design a smooth Lyapunov function quadratic in state variables and employ M -matrix theory to derive new stability conditions for genetic regulatory networks with time-varying delays. Theoretically, these conditions are less conservative than existing ones in some genetic regulatory networks. Then the results are extended to genetic regulatory networks with time-varying delays and noise perturbations. For genetic regulatory networks with n genes and n proteins, the derived conditions are to check if an n × n matrix is a non-singular M -matrix. To further present the new theories proposed in this study, three example regulatory networks are analysed.

In this short paper the problem of continuous time online estimation of frequency of a mixture of sinusoidal signal is considered. A simple estimator based on minimization of a Lyapunov function is suggested for the solution of this problem. For given a sinusoid signal consisting of many frequencies, the results show that estimator is globally convergent which can be applied for any initial condition and frequency values.

This paper characterizes the sum capacity of a class of potentially nondegraded Gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers. Coordination is allowed among the transmit terminals, but not among the receive terminals. The sum capacity is shown to be a saddle-point of a Gaussian mutual information game, where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information. The sum capacity is achieved using a precoding strategy for Gaussian channels with additive side information noncausally known at the transmitter. The optimal precoding structure is shown to correspond to a decision-feedback equalizer that decomposes the broadcast channel into a series of single-user channels with interference pre-subtracted at the transmitter.

This paper is concerned with the input-to-state stability (ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic nonlinear systems. By constructing a general SISS-Lyapunov function, which takes the exponential SISS-Lyapunov function as a special case, the ISS criteria are obtained respectively, for destabilizing and stabilizing impulses. It should be stressed that we impose the average dwell-time (ADT) condition for destabilizing impulses and reverse average dwell-time (RADT) condition for stabilizing impulses to restrain the occurrence of impulses, which extends the fixed dwell-time condition in recent literature. Moreover, the ADT and RADT conditions in this paper correspond to the average impulsive interval method in most existing results under exponential ISS-Lyapunov condition. As a subsequent result, the ISS and SISS of impulsive stochastic interconnected systems on networks are also studied by the Lyapunov method and graph-theoretical technique. Finally, several illustrative examples together with their numerical simulations are provided to demonstrate theoretical

In this paper, an adaptive fuzzy tracking control with filter-based event-triggered mechanism for stochastic nonlinear uncertain system suffered input hysteresis is presented. Considering stochastic disturbances and input hysteresis, Fuzzy Logic Systems (FLSs) are adopted to handle such issues. A time-varying vector contained weight vector and approximation error is established. Then, a class of smooth function is introduced to develop the adaptive control laws. It is aiming to avoid the chattering issue. Further, to achieve the desired tracking performance, this paper considers the discontinuous control input caused by the event-triggered control strategy. And the filter-based event-triggered strategy is presented. With the aid of Lyapunov function and Backstepping technique, the fuzzy event-triggered tracking control method is established for the considered system. It is testified that all signals are bounded under the action of the proposed method. Finally, the theoretical results are verified by the presented simulation examples.

After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user-friendly yet computationally efficient formulations for the analysis of complex MBS. The key to this is a holistic geometric approach to the kinematics modeling observing that the general motion of rigid bodies and the relative motion due to technical joints are screw motions. Moreover, screw theory provides the geometric setting and Lie group theory the analytic foundation for an intuitive and compact MBS modeling. The inherent frame invariance of this modeling approach gives rise to very efficient recursive $O ( n ) $ algorithms, for which the so-called “spatial operator algebra” is one example, and allows for use of readily available geometric data. In this paper, three variants for describing the configuration of tree-topology MBS in terms of relative coordinates, that is, joint variables, are presented: the standard formulation using body-fixed joint frames, a formulation without joint frames, and a formulation without either joint or body-fixed reference frames. This allows for describing the MBS kinematics without introducing joint reference frames and therewith rendering the use of restrictive modeling convention, such as Denavit–Hartenberg parameters, redundant. Four different definitions of twists are recalled, and the corresponding recursive expressions are derived. The corresponding Jacobians and their factorization are derived. The aim of this paper is to motivate the use of Lie group modeling and to provide a review of different formulations for the kinematics of tree-topology MBS in terms of relative (joint) coordinates from the unifying perspective of screw and Lie group theory.

In this paper, we analyze the existence and stability of equilibrium of DC micro-grids under the master-slave control (where some distributed generations (DGs) are under droop control(Droop-DGs) and some DGs are under MPPT control (MPPT-DGs)). Firstly, the power flow equation of the DC micro-grids under master-slave control with CPLs is obtained. Then, we transform the solvability of the power flow equation into the existence of a fixed point for a contraction mapping. Based on Banach' fixed point theorem, a sufficient condition to guarantee the existence of power flow solution in DC micro-grids is derived. The condition derived in this paper is not only useful for master-slave control but also for droop control. In addition, to calculate the power flow solution, an iterative algorithm with exponential convergence rate is proposed. Secondly, we use a small signal model to predict the qualitative behavior of the system near the equilibrium point. By analyzing eigenvalues of the system Jacobian matrix, the robust stable analytic conditions of the system are obtained. The obtained conditions provide a reference for establishing a reliable DC micro-grid. The simulation results verify the correctness of the proposed conditions.

In this paper, the multiple access channel (MAC) with channel state is analyzed in a scenario where a) the channel state is known non-causally to the transmitters and b) there is perfect causal feedback from the receiver to the transmitters. An achievable region and an outer bound are found for a discrete memoryless MAC that extend existing results, bringing together ideas from the two separate domains of MAC with state and MAC with feedback. Although this achievable region does not match the outer bound in general, non-trivial conditions are found where they meet. In the case of Gaussian MAC, a specialized achievable region is found by using a combination of dirty paper coding and a generalization of the Schalkwijk-Kailath (1966), Ozarow (1984) and Merhav-Weissman (2005) schemes, and this region is found to be capacity achieving. Specifically, it is shown that additive Gaussian interference that is known non-causally to the transmitter causes no loss in capacity for the Gaussian MAC with feedback

The operation of the multiple input multiple output (MIMO) Gaussian broadcast channel (BC) with K transmit antennas and K over r users with r receive antennas each is analyzed when channel state information (CSI) is obtained at the transmitter from the ith user via finite-rate feedback link of capacity B i bits. It is proved that if B i is scaled at the rate of α i r(K - r) log 2 P, where P is the transmit power and α ∈ [0, 1], then using dirty paper coding (DPC), the multiplexing gain of α i r can be achieved for user i. This result on the feedback scaling rate rests on an elegant achievability scheme, the construction of which brings to light several new insights on the manner in which DPC achieves the complete multiplexing gain in the perfect-CSIT case.

This paper deals with the stability analysis problem of continuous linear parameter varying (LPV) systems. The basic form of LPV systems are addressed in this paper and valuable results are proposed concerning the boundedness and stability concepts of these systems. A set of conditions are developed to explore the boundedness of LPV system based on some inherent properties of these systems. Then, the global stability problem of LPV systems is separately investigated based on the boundedness of the system. It has been mathematically proven that the stability conditions of LPV systems can be basically relaxed through the boundedness assumption. It has been shown the Lyapunov matrix of parameter dependent Lyapunov functions is not needed to be positive that surely reduces the conservativeness of the stability conditions. Finally, two illustrating examples are presented to explain all aspects of the results.

This paper proposes an optimal control design framework for hybrid nonlinear time-dependent dynamical systems involving an interacting mixture of continuous-time and discrete-time dynamics. Aiming to extend hybrid linear optimal control synthesis to nonlinear non-quadratic formulation, a hybrid version of the Hamilton–Jacobi–Bellman (HJB) equation with time-dependency is first presented. A hybrid computational framework, which alternates between continuous-time and discrete-time subsystems at an appropriate sequence of time instants, is then developed to solve the resultant set of the HJB equations in an interacting manner. The proposed control scheme is subsequently applied to spacecraft formation flying establishment with a hybrid source of actuation, namely Lorentz force and impulsive thrusting. By optimal combination of the Lorentz force and impulsive thrusting proposed in this paper, not only are the uncontrollability issues pertinent inherently to the Lorentz-actuated control systems effectively resolved, but use of both Lorentz and impulsive control inputs is also optimized. As a consequence, the expendable chemical fuels required to actuate thrusters are significantly reduced, thereby extending the duration of such space missions.

This paper addresses global stabilization of fractional-order memristor-based neural networks (FMNNs) with incommensurate orders and multiple time-varying delays (MTDs), where the time delay functions are not necessarily bounded. First, without assuming that time delay functions are bounded, the asymptotical stability condition is given for fractional-order linear positive system with incommensurate orders and MTDs. Then, comparison principle for such a system is established. By virtue of two kinds of vector Lyapunov functions (absolute-value-function-based and square-function-based vector Lyapunov functions), stability condition of fractional-order linear positive system and comparison principle, two stabilization criteria are derived and the equivalence between them is illustrated. In comparison with the reported criterion, the criteria derived in this paper are less conservative, since they allow controller parameters to satisfy weaker algebraic conditions. Lastly, numerical examples are displayed to validate the availability of the controller and correctness of the stabilization criteria.

In this paper, a robust H ∞ control problem of a class of linear parabolic distributed parameter systems (DPSs) with pointwise/piecewise control and pointwise/piecewise measurement has been investigated via the robust H ∞ feedback compensator design approach. A unified Lyapunov direct approach is proposed in consideration of the pointwise/piecewise control and point/piecewise measurement based on the distributions of the actuators and sensors. A new type of Luenberger observer is developed on the continuous interval of space domain to track the state of the system, and an H ∞ performance constraint with prescribed H ∞ attenuation levels is proposed in this paper. By utilizing Lyapunov technique, mathematical inequalities, and integration theory, a sufficient condition based on LMI for the exponential stability of the corresponding closed-loop coupled system under an H ∞ performance constraint is presented. Finally, the effectiveness of the proposed design method is verified by numerical simulation results.

This paper studies the distributed synchronization control problem of a class of stochastic dynamical systems with time-varying delays and random noise via randomly occurring control. The activation of the distributed adaptive controller and the update of the control gain designed in this paper all happen randomly. Based on the Lyapunov stability theory, LaSalle invariance principle, combined with the use of the properties of the matrix Kronecker product, stochastic differential equation theory and other related tools, by constructing the appropriate Lyapunov functional, the criterion for the distributed synchronization of this type of stochastic complex networks in mean square is obtained.

The paper illustrate the development and validation of two regression models i.e., poisson and artificial neural network employed to predict the significance of different climatic variables for an institutional building in composite climate. For prediction of outer wall temperature using five input parameters (ambient temperature, relative humidity, global radiation, wind speed and wind direction), two modeling approaches: poisson and artificial neural network were used. The results of both the model were validated through test data analysis in terms of three statistical measures namely, R-squared, root mean square error and mean absolute error. The performances of both the models are comparable in terms of train and test data. Comparative statistical analysis of both the model shows a better fit for the artificial neural network model as it was capable of adjusting themselves to the unpredicted changes in the input data. For the current study where weather parameters are continuously fluctuating poisson model was preferred as it generates the estimation coefficient values for the variables while neural model is not mathematically defined. The study demonstrates that neural model should be used as an alternative method for temperature prediction. The content and format of the paper has been widely used for designing and retrofitting of buildings by considering the most significant climatic variables for future work. Also, it helps the architects and engineers to find the relevant insulating material for the building envelope as per the requirement and subsequently improves its thermal behavior.

This paper proposes a novel predictive strategy based on a model predictive control (MPC) for the interior permanent magnet synchronous motors (IPMSMs) driven by a three-level simplified neutral-point clamped inverter (3L-SNPC) for electric vehicle applications (EVAs). Based on the prediction of the future behavior of the controlled variables, a predefined multiobjective cost function incorporates the control objectives which are evaluated for every sampling period to generate the optimal switching state applied directly to the inverter without the modulation stage. The control objectives in this paper are tracking current capacity, neutral-point voltage balancing, common-mode voltage control, and switching frequency reduction. The principal concepts of the novel scheme are summarized as follows: first, the delay compensation based on the long horizon of prediction is adopted by a multilevel power converter structure. Second, based on the modified Lyapunov candidate function, both stability and recursive feasibility are ensured of the proposed predictive scheme. Third, the practicability of the real-time implementation is improved by the proposed “static voltage vector” (SVV) and “single state variation” (SSV) principles. Finally, the proposed concepts are implemented in the novel predictive control formulation as additional constraints without compromising the complexity and the good performances of the predictive controller. Therefore, only the switching states that guarantee the stability and the reduction of calculation burden criteria are considered in the evaluation of cost function. The proposed predictive scheme based on the “SVV” principle has demonstrated superior performance in simulation compared with the proposed scheme with the “SSV” principle. The computational burden and switching frequency rates are reduced by 35% and 56.22%, respectively.

Although the time-domain aeroelastic analysis of the fin-actuator system is accurate, it is very time-consuming. Some work in the past used the describing function method to calculate the dynamic stiffness of the actuator, and then obtained the aeroelastic stability of the system in the frequency domain. This greatly shortened the time, but there was a loss in accuracy. In order to improve the accuracy and speed up the calculation to a certain extent, this paper uses high order harmonics to describe the response of the system. The frictional hysteresis loop is difficult to obtain a closed-form solution in the frequency domain. In this paper, a truncated Taylor series expansion is used to smooth the LuGre friction model so that the harmonic balance method can be used. The pseudo-arclength continuation method is used to solve the problem, and the bifurcation diagram of the limit cycle of the system is obtained. The results show that the method used in this paper has achieved a balance between time and accuracy in calculating the aeroelastic stability of the fin-actuator system.

In the paper, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability analysis method are further revealed. It is interesting to show that some unstable impulsive time-delay systems may be stabilized by increasing the time delay in continuous dynamics. More interestingly, it is proved that along with the increase of the delay within a certain range, the convergence rate of such impulsive timedelay systems also increases correspondingly. Further, a strict comparison principle for impulsive control systems with delay is established. Then by utilizing this comparison principle, it can be shown that for some stable impulsive systems with delay, under certain conditions, the stability is robust against any large but bounded delay. Compared with the previous results on delay-free impulsive systems, some potential impacts of delay on the stability are investigated. Particularly, the obtained results are extended to the case of impulsive control systems with hybrid im

This paper addresses fuzzy control design for a class of nonlinear systems which are described by nonlinear ordinary differential equations (ODEs) cascaded with an Euler-Bernoulli beam (EBB) equation. Two design difficulties are involved in the control design addressed in this paper. The first one is caused by the EBB equation whose spatiotemporal dynamics is affected by the output of the nonlinear ODE subsystem through its differential equation rather than boundary conditions. A state differential transformation is introduced for the EBB equation to bring the output of the ODE subsystem in the differential equation to its boundary conditions. The second one comes from the nonlinear ODE subsystem. To overcome this difficulty, it is assumed that an exact Takagi-Sugeno (T-S) fuzzy ODE model is utilized by the sector nonlinearity approach to describe the dynamics of nonlinear ODE subsystem. Based on the T-S fuzzy model, a composite Lyapunov function is constructed to develop a fuzzy controller via the ODE state feedback and boundary feedback of transformed EBB equation to exponentially stabilize the nonlinear ODE-EBB cascaded system. The design procedure is presented in terms of bilinear matrix inequalities (BMIs). Moreover, a simple design method is also provided in terms of linear matrix inequalities (LMIs) from the obtained design procedure. Finally, numerical simulations on flight control with vibration suppression of a flexible air-breathing hypersonic vehicle are given to illustrate the effectiveness of the proposed design method.

This paper focuses on the state estimation issue of T–S fuzzy Markovian generalized neural networks (GNNs) with reaction–diffusion terms. An estimator-based nonfragile time-varying proportional retarded sampled-data controller that permits norm-bounded indeterminacy and contains a time-varying delay is designed to guarantee the asymptotical stability of the error system. By establishing a novel Lyapunov–Krasovskii functional that involves positive indefinite items and discontinuous items, meanwhile, by combining the reciprocally convex combination method, Jenson’s inequality and Wirtinger inequality, a less conservative stability criterion can be derived. Moreover, the principle for the number of selected variables in the process of deriving main results is also analyzed. Finally, two numerical examples are given to demonstrate the validity and advantages of the results proposed in this paper.

In this paper, we analyze the problem of the stabilization for discrete-time Takagi–Sugeno fuzzy parametric uncertain systems. The stabilization conditions of these systems are investigated with two observers and two different Lyapunov functions: nonquadratic and delayed nonquadratic. The stabilization conditions are analyzed between k and k + t sample variations in the Lyapunov function. The obtained stabilization results represent an extension of previous works with one-sample variation in discrete time. All the results are obtained in the form of linear matrix inequalities which are solved by using various convex optimization algorithms. Two theorems are proposed, and comparison via simulation is given to demonstrate the robustness of the proposed approaches. Nevertheless, this paper shows that the second proposed observer gives the less conservative results (less restrictive). These reduced conservative results are demonstrated by a larger feasible area of stabilization (stabilization domain) and a fast convergence of estimation errors compared to the first.

This paper investigates a novel nonrecursive tracking control law design for a class of nonlinear systems via dynamic output feedback. As the main contribution of this paper, a global nonrecursive tracking design procedure is first proposed to render a simple construction of a realizable output feedback control law, whose gain selections follow the conventional pole placement approach while the stability margin can be guaranteed via a sufficiently large scaling gain. By introducing a Lyapunov function which neglects the virtual controllers in essence, rigorous analysis is presented to ensure the global stability. In addition, finite-time and asymptotical tracking results can now be achieved within the same design framework whereas the tunable homogeneous degree plays as a key role. As another contribution, by proposing a saturated dynamic compensator, a less ambitious but practical control objective, namely semiglobal stability is achieved of the closed-loop system to relax the requirement of the restrictive growth conditions for global control design. Taking consideration of the case when system is subject to mismatched disturbances, a unified design and stability analysis framework shows that the practical tracking result can also be realized. A numerical example is provided to illustrate the effectiveness of the nonrecursive design and the simplicity of the proposed tracking control algorithm. This work was supported by the National Natural Science Foundation of China under Grant 61503236, Grant 61473080, and Grant 61573099.

This paper deals with the stability, stabilization and ${L_{2}} - $ gain problem of periodic piecewise impulsive linear system. Firstly, by developing a new Lyapunov function called multiple piecewise time-varying Lyapunov function, a sufficient condition that guarantee the system $\mathop \lambda \nolimits ^{*} - $ exponentially stable is established. Moreover, a state-feedback controller is designed to stabilize the system. Then ${L_{2}} - $ gain analysis is investigated to obtain a result that guarantee the system $\mathop \lambda \nolimits ^{*} - $ exponentially stable and with ${L_{2}} - $ gain performance. Finally, numerical simulation examples are provided to verify the effectiveness of the results proposed in this paper.

One of the main issues related to integral control is windup, which occurs when, possibly due to a fault, the input signal u of the plant reaches a value outside the allowed input range U. This paper presents an integral controller with anti-windup, called saturating integrator, for a single-input single-output nonlinear plant having a curve of locally exponentially stable equilibrium points that correspond to constant inputs in U. A closed-loop system is formed by connecting the saturating integrator in feedback with the plant. The control objective is to make the output signal y of the plant track a constant reference r, while not allowing its input signal u to leave U. Using singular perturbation methods, we prove that, under reasonable assumptions, the equilibrium point of the closed-loop system is exponentially stable, with a “large” region of attraction. Moreover, when the state of the closed-loop system converges to this equilibrium point, then the tracking error tends to zero. A step-by-step procedure is presented to perform the closed-loop stability analysis, by finding separately a Lyapunov function for the reduced (slow) model and a Lyapunov function for the boundary-layer (fast) system. Afterwards, a Lyapunov function for the closed-loop system is built as a convex combination of the two previous ones, and an upper bound on the controller gain is found such that closed-loop stability is guaranteed. Finally, we show that if certain stronger conditions hold, then the domain of attraction of the stable equilibrium point of the closed-loop system can be made large by choosing a small controller gain.

In this paper, sampled-data control is proposed to stabilize the nonlinear system, which is expressed as a Takagi–Sugeno (T–S) fuzzy submodels. Based on suitable Lyapunov– Krasovskii functional (LKF) along with new weighted integral inequalities, the sufficient conditions are derived in terms of linear matrix inequalities, which ensure the exponential stability of the proposed closed loop T–S fuzzy system. The peculiarity of this paper is: as novel integral inequalities and LKF are proposed, less conservative results are provided when compared to existing results. Besides that, wind energy conversion systems, chaotic systems, and an inverted pendulum are validated with derived sufficient conditions. The corresponding simulation results show the merit of the proposed results over the existing works.

In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative (PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally, numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.

At this time, there is a widespread use of numerical control lathes, which aims to develop technical solutions for automatic control of the state of the technological system, in particular the tool. In the process of cutting, the cutter fails as a result of a dull (end of durability period), breaks (complete destruction of the cutting edge or crumbles into particles of cutting material), softens (loss of hardness in steel and welding are almost unobservable in hard alloy) and, in the end, the result is increased wear.At the same time, the main requirement is a higher reliability of the results obtained, this is largely determined by the chosen methods of information analysis, which characterizes the state of the technological system. Durability of the tool should provide high performance and the lowest material costs associated with the manufacture of the product. This resistance is called economic. Its approximate values for different cutting tools, adopted in the standards for cutting conditions, are given in the relevant directories.The most promising methods are synergistic. One of the most important results of synergetics was the conclusion that the length of the time horizon of the prediction of circulation was limited even for relatively simple systems. This applies to systems that are sensitive to initial conditions. The main task is to choose a characteristic or group of characteristics by which it is supposed to evaluate the state of the processing system and establish the dependence of the selected characteristic on time. As the initial data it is supposed to use a vibrosignal which is generated by the process of turning, as the initial data – wear of the cutter.Calculations of cross-correlation showed that its value reaches 0.72 Ra/μm, which indicates the presence of a relationship between the values. Three characteristic areas can be identified. In the first region there is an intensive increase in the values of the Lyapunov index. In the second area, there are slight fluctuations in the indicator values, and when a certain wear chamfer threshold is reached - changes in the Lyapunov indicator values are extremely small (about 10-5 ... 10-6) – this area corresponds to a period of catastrophic wear.As established during the study was observed in all the experiments carried out at the finishing turning. Analyzing the obtained results, we can conclude that the use of the Lyapunov indicator is justified for tracking the pathological changes in the mill of the technological processing system – that is, by the value of the Lyapunov indicator, one can judge the occurrence or non-occurrence of catastrophic tool wear., В настоящее время наблюдается широкое применение токарных станков с числовым программным управлением, которое ставит цель разработать технические решения автоматического контроля состояния технологической системы, в частности инструмента. В процессе резания резец выходит из строя в результате затупления (конец периода стойкости), поломки (полное разрушение режущей кромки или крошение на частички режущего материала), размягчения (потеря твердости в стали – явление, почти не наблюдаемое у твердого сплава) – в результате показатель износа увеличивается.При этом основным требованием является более высокая достоверность полученных результатов, это во многом определяется выбранными методами анализа информации, которая характеризует состояние технологической системы. Стойкость инструмента должна обеспечивать высокую производительность и наименьшие материальные затраты, связанные с изготовлением изделия. Такую стойкость называют экономической. Ее ориентировочные значения для разных режущих инструментов приводятся в соответствующих справочниках.Наиболее перспективными методами есть синергетические. Одним из самых важных результатов синергетики стал вывод относительно принципиальной ограниченности длины временного горизонта прогноза обращения даже для сравнительно простых систем. Это касается систем, чувствительных к начальным условиям. Основной задачей является выбор характеристики или группы характеристик, по которым предполагается оценивать состояние обрабатывающей системы, и определение зависимости избранной характеристики от времени. В качестве исходных данных предполагается использовать вибросигнал, который генерируется процессом токарной обработки.Расчеты взаимной корреляции показали, что ее величина достигает 0.72 Ra/мкм, что говорит о наличии зависимости между величинами. Можно выделить три характерных области. В первой области наблюдается интенсивный рост значений показателя Ляпунова, во второй области – незначительные флюктуации значений показателя, а при достижении определенного порога фаски износа – изменения значений показателя Ляпунова крайне небольшие (порядка 10-5 ... 10-6) – данная область отвечает периоду катастрофического износа.Как было установлено в ходе исследования, упомянутая выше зависимость наблюдалась при проведении всех экспериментов при чистовом точении. Анализируя полученные результаты, можно сделать вывод, что применение показателя Ляпунова оправдано для отслеживания патологических изменений состояния технологической системы, т.е. по значению показателя Ляпунова можно судить о наступлении или отсутствии катастрофического износа инструмента., На даний час спостерігається все більш широке застосування токарних верстатів з числовим програмним керуванням, яке ставить за мету розробку технічних рішень автоматичного контролю стану технологічної системи, зокрема інструменту. В процесі різання різець виходить з ладу в результаті затуплення (кінець періоду стійкості), поломки (повне руйнування різальної кромки або викришування частинок ріжучого матеріалу), розм’якшення (втрата твердості у сталі – явище, яке майже не спостерігається у твердому сплаві) – в результаті показник зносу збільшується. Характер зносу і його вплив на процес різання можуть бути різними.При цьому основною вимогою є якомога більш висока достовірність отриманих результатів, що багато в чому визначається обраними методами аналізу інформації, яка характеризує стан технологічної системи. Стійкість інструменту повинна забезпечувати високу продуктивність і найменші матеріальні витрати, пов’язані з виготовленням виробу. Таку стійкість називають економічною. Її орієнтовні значення для різних різальних інструментів наводяться у відповідних довідниках.Найбільш перспективними методами є синергетичні, найпоширенішими серед яких є методи нелінійної динаміки.Одним із найважливіших результатів синергетики є висновок щодо принципової обмеженості довжини часового горизонту прогнозу звернення навіть для порівняно простих систем. Це стосується систем, чутливих до початкових умов. Основним завданням є вибір характеристики або групи характеристик, за якими передбачається оцінювати стан системи, і визначення залежності обраної характеристики від часу. В якості вихідних даних передбачається використовувати вібросигнал, який генерується процесом токарної обробки.Розрахунки взаємної кореляції показали, що її величина сягає 0.72 Ra/мкм, що говорить про наявність залежності між величинами. Можна виділити три характерні області. У першій області спостерігається інтенсивне зростання значень показника Ляпунова, у другій області – незначні флуктуації значень показника, а при досягненні певного порогу фаски зносу – зміни значень показника Ляпунова вкрай невеликі (близько 10-5 ... 10-6) – дана область відповідає періоду катастрофічного зносу.Як було встановлено в ході дослідження, зазначена вище залежність спостерігалася при проведенні всіх експериментів при чистовому точінні. Аналізуючи отримані результати, можна зробити висновок, що застосування показника Ляпунова виправдано для відстеження патологічних змін стану технологічної обробної системи, тобто за значенням показника Ляпунова можна судити про настання чи відсутність катастрофічного зносу інструменту.

This paper proposes a decoupling tracking controller for quadrotors using dynamic surface control (DSC) and second-order sliding mode disturbance observer (SMDO). The DSC used in this paper is improved with the sliding mode differentiators that replace the original low-pass filter, and the SMDO is utilized to restrain the influence of system uncertainties and external disturbances. In addition, instead of the roll attitude angle ( $$\varphi $$ ) and pitch attitude angle ( $$\theta $$ ), applying $$\sin {\varphi }$$ and $$\sin {\theta }$$ as control variables simplifies the analysis of stability. Moreover, a fuzzy logic-based method is utilized to compensate the influence of battery voltage changing during the procedure of thrust generation. The asymptotic tracking property of the closed-loop system is proven via the Lyapunov-based stability theory. Finally, the real-time experiment results, which contain a hovering case and rectangular path tracking case, are given to validate the practicability of the proposed method.

Purpose This paper aims to propose an analytical method for designing parametric optimization-based proportional integral (PI) controllers. Design/methodology/approach In this method, a performance index containing the weighted summation of the integral square of the error and its derivative is minimized. This performance index is analytically calculated in terms of the controller parameters by solving a Lyapunov equation. Then partial derivatives of the performance index with respect to controller parameters are calculated. Equating these partial derivatives to zero gives explicit relations for the PI controller parameters. Findings The experimental tests on a DC servomotor system are given to demonstrate the efficiency of the proposed method. Originality/value This paper proposes an analytical parametric optimization approach for designing PI controllers for the first time. The application of the proposed method in a laboratory experiment is examined.

This paper focuses on the the problem of $L_{\infty}$ tracking controller design for T-S fuzzy systems with external disturbance. Firstly, by the use of the information of the state of the controlled plant and the reference model, a tracking controller is synthesized to ensure that the state of the controlled plant can well track the state of reference model. Second, to increase the performance of tracking control, the design methods of the tracking controller based on the $L_{\infty}$ performance index is proposed. Unlike, some conventional $H_{\infty}$ control methods, where the reference signal should be energy-bounded, the abovementioned constraint is removed in this paper by using the proposed $L_{\infty}$ tracking control method. Furthermore, the controller gain matrices are obtained by Lyapunov analysis method. Finally, simulation results are given to show the good tracking control performance of the developed approach.

In recent years there have been numerous studies of reception or communications systems for the demodulation of signals which are received with additive gaussian noise. Many of these studies have been based on the work of Youla. In FM modulation the signal is subjected to linear filtering (pre-emphasis) prior to modulation and it is not immediately apparent how to apply the work of Youla directly. Linear filtering prior to modulation is also used in many other situations which occur in practice (for example, SSB AM can be produced by a combination of linear operations on the signal), and it is therefore pertinent to extend Youla?s work to this case. The purpose of this communication is to point out that Youla?s work can be extended in a straightforward way to cover modulation schemes in which filtering prior to modulation is employed. The results have been known for some time but apparently are not widely available.

This research focuses on the ride comfort of passengers in vehicles equipped with passive suspension systems. To ensure ride comfort, the paper proposes predicting the vehicle's appropriate velocity that drivers should sustain before approaching speed humps. Support Vector Machines, a powerful Machine Learning tool, is used to predict the appropriate vehicle velocity. A simulation technique was used to build the dataset for the learning process; an adequate velocity was found for each hump shape. The K-folds cross validation technique was applied to 80% of the dataset using three types of Support Vector Machine kernel functions: linear, polynomial, and Gaussian kernels. The results of the validation showed very good performance of the three kernel functions. However, Gaussian kernel function performed best, with a correlation coefficient (R) of 0.998, a mean absolute error (MAE) of 0.383, and a root mean square error (RMSE) of 0.247. The final test was performed on the remaining 20% of the dataset and the predicted velocity was compared with the simulated one. The results showed excellent performance, with an error that is less than 3% for velocity greater than 6 Km/h.

Fast scale stability of Dual active bridge (DAB) converter with input filter under constant power load (CPL) is analyzed in this paper. Since the commonly used reduced-order average model is not effective to accurately describe the dynamic behavior of DAB converter, a discrete-time model is established. The bifurcation points of the system are predicted by using bifurcation diagrams. In addition, Poincar map theory and the Jacobian matrix of the system are used for bifurcation analysis. The eigenvalue locis of Jacobian matrix are carried. Serval Hopf bifurcations and a saddle-node bifurcation, which are predicted by the eigenvalue locis, have been found in the converter. The influence of system parameters on the stability of the system is explained in detail. It is found that high output voltage bandwidth, input filter and light-load are the main causes of instability in this system. To stabilize the converter, a proper feedback control is presented. In addition, stable boundaries are given to help to avoid instability. All the findings have been verified by simulation and experimental results.

This paper shows that the SIR model of infectious diseases is input-to-state stable (ISS) with respect to the net flow of susceptible individuals into the region in both disease-free and epidemic situations. The key development is the construction of a continuously differentiable strict Lyapunov function. Firstly, for asymptotic stability, this paper clarifies that a continuously differentiable Lyapunov function can deduce the stability on the whole state space even if its derivative is not strictly negative. Secondly, it is demonstrated that a new idea of modifying the Lyapunov function to render its derivative strictly negative allows one to detect an appropriate margin to prove ISS of the SIR model. The accomplishment is based on the pursuit of a Lyapunov function which is not entirely separable into components. It contrasts with previously studied and popular Lyapunov functions which are incapable of assessing robustness properties such as ISS.

This paper mainly studies the stability and Hopf bifurcation criteria of hub-based genetic regulatory networks with multiple delays and bidirectional couplings. The hub-structured network is an important motif in complex networks, which provides a new view angle on structure to describe the regulation mechanism between genes (including both mRNAs and proteins). It is well known that hubs play a leading role in characterizing the network dynamical behaviors. However, the dynamics of hubs or star-coupled systems is not well understood. In this paper, we first examine the existence of the positive equilibria in this type of genetic networks. By analyzing the associated characteristic equation, we present sufficient conditions of biochemical parameters for delay-independent local stability in hub-coupled genetic regulatory networks. Then we investigate their Hopf bifurcation when such networks lose their stability. Specific conditions for delay-dependent stability and Hopf bifurcations in genetic networks with hub structure are derived. It is found that the dynamics of hub-structured genetic regulatory networks has no direct relationship with single time delay or individual connection, but instead depends on the sum of all delays among all genes and the product of the connection strengths between all genes. Finally, some simulation examples are provided to substantiate our analysis.

Piezoelectric actuators (PEAs) are increasingly applied to the field of ultraprecision positioning; however, unwanted nonlinearities, such as hysteresis, degrade their performance. This paper integrates a Gaussian process (GP) with a Maxwell-slip (MS) model to capture nonlinearities in PEAs. The GP predicts the output of a PEA or the error of the MS model by using the current and historical applied input voltages, as well as the measured historical output displacements, as input. The measured output is replaced by the output of the MS model in the case that a displacement sensor is unavailable. The experimental results show that by properly selecting system order, the proposed approach achieves a precise result and provides the boundary of the prediction error in terms of variance. If the output displacement is available and the GP predicts the output of a PEA directly, the normalized root mean square error (NRMSE) is as low as 0.29%. The NRMSE is reduced further to 0.14\% if the data set used for prediction is updated online.

The estimation of system state is pivotal especially when system state can't be directly measured. In this paper, an optimal robust observer is proposed for uncertain dynamical systems. The fuzzy set theory is utilized to interpret the uncertainty bound. Unlike fuzzy-logic based observer, the proposed observer is not IF-THEN fuzzy rules-based. The uniform boundedness and ultimate uniform boundedness of estimation error are guaranteed. Then, the optimal design problem of the two tunable parameters is formulated under the framework of a two-player Nash game. The fuzzy-set theoretic cost functions of the two players are associated with the observer performance. We prove that the Nash equilibria does exist, and provide procedures in solving this optimal problem. Numerical simulations are conducted on an inverted pendulum using MATLAB/Simulink. The theory is illustrated by the observer design for an inverted pendulum subject to the earthquake excitation. The novelty of this work is an integrated framework for optimal robust observer design, which creatively blends the state estimation theory, the fuzzy set theory and the Nash game theory.

In this paper, the locally fixed-time and globally fixed-time stabilization problems for the port-Hamiltonian (PH) systems via the interconnection and damping assignment passivity-based control technique are discussed. The definitions of fixed-time stability region (or region of attraction) and fixed-time stability boundary are given in this paper. From this starting point, the sufficient condition of globally fixed-time attractivity of a prespecified locally fixed-time stability region is obtained. Combining the locally fixed-time stability and the globally fixed-time attractivity of a prespecified locally fixed-time stability region, the globally fixed-time stabilization problem for PH system is effectively solved. Furthermore, the globally fixed-time control scheme independent of locally fixed-time stability region has also been derived by constructing a novel Lyapunov function. A illustrative example shows that the results obtained in this paper work very well in fixed-time control design of PH systems.

Purpose To meet the need of reducing the cost of industrial systems, sensorless control applications on electrical machines are increasing day by day. This paper aims to improve the performance of the sensorless induction motor control system. To do this, the speed observer is designed based on the combination of the sliding mode and the fractional order integral. Design/methodology/approach Super-twisting sliding mode (STSM) and Grünwald–Letnikov approach are used on the proposed observer. The stability of the proposed observer is verified by using Lyapunov method. Then, the observer coefficients are optimized for minimizing the steady-state error and chattering amplitude. The optimum coefficients (c1, c2, ki and λ) are obtained by using response surface method. To verify the effectiveness of proposed observer, a large number of experiments are performed for different operation conditions, such as different speeds (500, 1,000 and 1,500 rpm) and loads (100 and 50 per cent loads). Parameter uncertainties (rotor inertia J and friction factor F) are tested to prove the robustness of the proposed method. All these operation conditions are applied for both proportional integral (PI) and fractional order STSM (FOSTSM) observers and their performances are compared. Findings The observer model is tested with optimum coefficients to validate the proposed observer effectiveness. At the beginning, the motor is started without load. When it reaches reference speed, the motor is loaded. Estimated speed and actual speed trends are compared. The results are presented in tables and figures. As a result, the FOSTSM observer has less steady-state error than the PI observer for all operation conditions. However, chattering amplitudes are lower in some operation conditions. In addition, the proposed observer shows more robustness against the parameter changes than the PI observer. Practical implications The proposed FOSTSM observer can be applied easily for industrial variable speed drive systems which are using induction motor to improve the performance and stability. Originality/value The robustness of the STSM and the memory-intensive structure of the fractional order integral are combined to form a robust and flexible observer. This paper grants the lower steady-state error and chattering amplitude for sensorless speed control of the induction motor in different speed and load operation conditions. In addition, the proposed observer shows high robustness against the parameter uncertainties.