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This paper investigates the non-fragile robust H ∞ control problem of nonlinear uncertain neutral stochastic Takagi–Sugeno (T–S) fuzzy systems with mixed time-delays. The uncertainties are norm-bounded and time-varying. Sufficient conditions for H ∞ performance analysis results of the delay-dependent condition is established via the Lyapunov–Krasovskii functional (LKF) technique and linear matrix inequality (LMI) method. Based on the H ∞ performance result, a desired fuzzy control is designed by solving LMIs. Finally, an example is provided to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the issue of finite-time observer-based H ∞ control design of networked switched systems (NSS) subject to external disturbances via an event-triggered observation strategy. This triggering strategy is used to decide when the output measurements are sent to the observer over the communication network. By incorporating digital networks, the closed-loop system is modeled as a switched delayed system due to network-induced delays. By using the average dwell time (ADT) switching method with the Lyapunov–Krasovskii functional, several sufficient linear matrix inequalities (LMIs) conditions for the observer-based control synthesis are developed to guarantee the finite-time boundedness and the disturbance attenuation control performance of the resulting switched delayed system. Finally, an example is given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The stability and dynamic performance of the system are impacted by the uncertainties present in the converter model and controller parameters. This paper introduces a robust non-fragile control approach that addresses the influence of these uncertainties. The approach involves developing a control law that achieves quadratic stabilization of the closed-loop system while also satisfying the H∞ norm constraint for disturbance attenuation. Based on this concept, a robust non-fragile PI controller is designed explicitly for voltage mode control of a dc–dc buck converter. The effectiveness of the proposed control technique is evaluated from two perspectives: (i) its ability to withstand significant perturbations in plant parameters and load disturbances and (ii) its resilience in the presence of variations in controller parameters. The effectiveness of the proposed control scheme is validated using simulation and experimental results. [ABSTRACT FROM AUTHOR]

This paper considers a linear continuous- or discrete-time dynamic object in the absence of its mathematical model. As is demonstrated below, a control law that suboptimally damps initial and (or) exogenous disturbances of such objects can be implemented based on experimental and a priori data. The approach involves the methods of robust control design and duality theory as well as the technique of linear matrix inequalities. [ABSTRACT FROM AUTHOR]

The Takagi–Sugeno (T–S) fuzzy model is a versatile approach widely used in system control, often in combination with other strategies. This paper addresses key control challenges linked to the T–S system and presents important considerations to ensure its successful application using the Lyapunov theorem. One crucial aspect is determining the optimal number of premise variables and selecting accurate fuzzy rules for the T–S model. Additionally, the theorem based on Linear Matrix Inequality (LMI) is developed to enable effective disturbance rejection. To enhance stability control, constraints are imposed on the output angle and control input of a rotary inverted pendulum (RIP). By integrating T–S fuzzy control, disturbance rejection, and input/output constraints, robust stability in controlling the RIP is achieved. Extensive simulations are performed to showcase the efficiency of the suggested method, and the simulation results are thoroughly discussed and analyzed to verify the efficacy of the control method. [ABSTRACT FROM AUTHOR]

In this paper, the desired yaw orientation for an autonomous underwater vehicle is attained by acquiring a cascaded control structure based on a robust optimal control algorithm with a backstepping approach. A robust state feedback optimal control law is designed to control the yaw rate. Hence, the desired yaw rate is intended to be obtained by the backstepping controller by controlling the desired yaw orientation. The implementation of the proposed robust control algorithm is formulated by using semi-definite programming. A linear quadratic regulator in terms of linear matrix inequality is designed to address the control problem. The design of robust optimal control law in the steering plane is achieved by considering an uncertain polytopic AUV system. Realization of the proposed control algorithm is conducted in MATLAB/Simulink environment using the YALMIP tool. Robust behavior is ensured by the proposed control algorithm while tracking the desired yaw. The robustness analysis is extended by considering the various ranges of specific uncertain parameters to highlight the efficacies of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

The Takagi–Sugeno (T–S) fuzzy model is a versatile approach widely used in system control, often in combination with other strategies. This paper addresses key control challenges linked to the T–S system and presents important considerations to ensure its successful application using the Lyapunov theorem. One crucial aspect is determining the optimal number of premise variables and selecting accurate fuzzy rules for the T–S model. Additionally, the theorem based on Linear Matrix Inequality (LMI) is developed to enable effective disturbance rejection. To enhance stability control, constraints are imposed on the output angle and control input of a rotary inverted pendulum (RIP). By integrating T–S fuzzy control, disturbance rejection, and input/output constraints, robust stability in controlling the RIP is achieved. Extensive simulations are performed to showcase the efficiency of the suggested method, and the simulation results are thoroughly discussed and analyzed to verify the efficacy of the control method. [ABSTRACT FROM AUTHOR]

This paper develops a novel unified approach to designing suboptimal robust control laws for uncertain objects with different criteria based on a priori information and experimental data. The guaranteed estimates of the γ0, generalized H2, and H∞ norms of a closed loop system and the corresponding suboptimal robust control laws are expressed in terms of solutions of linear matrix inequalities considering a priori knowledge and object modeling data. A numerical example demonstrates the improved quality of control systems when a priori and experimental data are used together. [ABSTRACT FROM AUTHOR]

This work proposes a dimmable high-power factor LED driver operating from universal mains voltage range (90–264 V). In order to ensure stability and good dynamic response, for all operating points, a robust state feedback controller is used. Additionally, a H ∞ optimization is employed to attenuate the undesired output current low-frequency ripple. The controller's design is carried out by means of linear matrix inequalities (LMIs). In order to validate the theoretical analysis, a 34 W integrated off-line buck–boost flyback converter prototype was built. The results have shown the capability of the control scheme of ensuring robust stability and performance throughout the whole operating range, as well as providing an output current ripple attenuation of about 66%. [ABSTRACT FROM AUTHOR]

To improve the anti-disturbance stability of the autonomous underwater vehicles (AUVs) under bounded disturbances in amplitude, we develop a robust controller based on the estimated signals generated by the filter. The AUV studied has the characteristics of time-varying delay, under-actuated, and switched linear parameter varying (LPV) dynamics. Both the filter and the control strategies, we proposed are based on the robust L 1 performance criterion, which is suitable for the amplitude-bounded disturbances in the ocean environment. In the filter and controller design, the corresponding Lyapunov–Krasovskii functional is established to verify the stability of the systems. As there exist couplings between the designed functional and the system parameter matrices, slack matrices are constructed for decouplings after validating the stability of the under-actuated AUV filtering error system and closed-loop control system. The filter and the controller are obtained in the form of parameter linear matrix inequalities (PLMIs), whose solution is infinite-dimensional matrix inequalities. The approximate basis function and gridding technique are applied to transform the filter and the controller into that of finite dimensional LMIs. The simulation has verified the effectiveness of the robust L 1 filter and anti-disturbance depth robust L 1 controller. [ABSTRACT FROM AUTHOR]

This paper suggests an observer based control approach for fully active hybrid energy storage system (HESS) comprising of two storage elements such as supercapacitor (SC) and battery, two bidirectional DC–DC converters and variable load. In order to formulate a control approach for this hybrid system, the unmeasured dynamics of the system must be available. This engenders the design of a robust exponential state observer in this paper to estimate various unknown system variables such as load, battery and SC currents/voltages. Furthermore, this paper also renders an integral terminal sliding mode control (ITSMC) concatenated with Proportional Integral (PI) based Lyapunov's function technique to robustly track the reference battery current, SC current and load voltage in finite time in the presence of lumped system uncertainties. The robustness, stability and finite time convergence properties of the closed loop system with the proposed technique are demonstrated through analytical approach. Simulated results are validated with the proposed methodology through various case studies and compared with LMI (linear matrix inequalities) based robust control techniques presented in literature. [ABSTRACT FROM AUTHOR]

This paper studies the problem of event-triggered robust H ∞ control for a class of networked flight control systems (NFCSs), in which parameter uncertainties and actuator failures are jointly involved. Firstly, under networked environments, we design an adaptive event-triggered mechanism (AETM) in order to reduce the data transmissions, whose triggering thresholds can be dynamically adjusted to real-time variations of NFCSs. Secondly, based on AETM and state feedback controller, a closed-loop model can be obtained and an augmented Lyapunov–Krasovskii functional can be further constructed. Thirdly, by means of two effective inequalities, some sufficient conditions on designing the AETM and controller are expressed via linear matrix inequalities, which can ensure the NFCSs to achieve control target and lead to less conservatism. Finally, a numerical example is presented to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

A discrete-time robust fuzzy controller design problem for the discretized and perturbed nonlinear ship fin stabilizing systems is studied in this paper. The discrete-time Takagi–Sugeno fuzzy model is used to represent the nonlinear ship fin stabilizing systems. The control performance considered in this paper includes stability requirement, pole location constraint, individual state variance constraint, and minimum output variance. Applying the Lyapunov theory, a discrete-time robust fuzzy controller is designed based on parallel distributed compensation technology and the relevant conditions are deduced in the form of linear matrix inequalities. By solving these conditions, a discrete-time robust fuzzy controller can be obtained to satisfy the above performance constraints. At last, a simulation for controlling a discrete-time nonlinear ship fin stabilizing system is provided to show the feasibility and applicability of the proposed robust fuzzy control method. [ABSTRACT FROM AUTHOR]

For a class of uncertain differential spatially interconnected systems in the particular case of active electrical ladder circuits, the problem of iterative learning control with stability and robust performance specifications in finite frequency ranges is investigated in this paper. Firstly, the dynamics are converted to an equivalent differential linear repetitive process. Then, based on the Kalman–Yakubovich–Popov Lemma, a control law design algorithm is presented in the form of the corresponding linear matrix inequalities. Since the system parameters are norm-bounded uncertain, an extension to robust control law is also discussed. The resulting dynamics satisfy the robust performance specifications, and the error monotonically converges in finite frequency ranges with the robust iterative learning control law. Finally, a control simulation of an active electrical ladder circuit is presented to illustrate the advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a stabilizing state feedback controller for a class of nonlinear time-delay descriptor system over the finite-time interval. The considered system is exposed to parameter uncertainties and time-varying disturbances. To provide a wider and more general class of nonlinear time-delay descriptor systems, the nonlinear parts of the system are assumed to be a function of state variables, delayed state variables, input and also delayed input and to satisfy the one-sided Lipschitz condition. The purpose of finite-time control is to propose a robust control law such that the resulting closed-loop system is stable, impulse free and regular for all admissible model uncertainties over the considered time interval. Additionally, the designed controller ensures the H ∞ disturbance attenuation of the closed-loop descriptor system. In order to achieve these goals, two theorems are given. The sufficient conditions are gained based on the delay-dependent analyses. These conditions then are converted to solvable linear matrix inequalities (LMIs). Finally, simulations are provided a practical example, to confirm the theoretical achievements. The practical example is a partial element equivalent circuit which is a neutral time-delay system. This system is transformed into a time-delay descriptor system. Simulation outcomes illustrate the effective performance of the given method in robust finite-time stabilization. [ABSTRACT FROM AUTHOR]

This paper focuses on the path-tracking controller design for autonomous ground vehicles (AGVs) using four-wheel steering (4WS) and direct yaw-moment control (DYC) systems. In order to deal with the parametric uncertainties, a linear parameter-varying (LPV) H∞ controller is designed as the high-level controller to generate the front and rear wheel steering angles and external yaw moment based on linear matrix inequality (LMI) approach. The lower-level controller is designed for torque allocation between the left and right side wheels to yield the desired total longitudinal force and external yaw moment utilizing weighted least square (WLS) allocation algorithm. To test the performance of the proposed path-tracking controller, numerical simulations are carried out based on a high-fidelity and full-vehicle model constructed in CarSim. Simulation results show that the LPV/H∞ controller has better path-tracking performance than the fixed gain H∞ controller. To show the superiority of 4WS+DYC control system, the contrast simulation is performed based on LPV/H∞ controller. Simulation results indicate that 4WS+DYC control system has better path-tracking performance and handling stability than active front steering (AFS), AFS+DYC and 4WS control systems. [ABSTRACT FROM AUTHOR]

This paper studies the finite-time stabilization of a class of time-delay nonlinear systems in the presence of uncertainties and external disturbances under the input amplitude constraints. The external disturbances are unknown and energy-bounded and the nonlinear vector function of system satisfies the one-sided Lipschitz condition which is less conservative than the well-known Lipschitz condition. To have a robust finite-time stabilization in the considered system, a robust H∞ controller is designed with respect to a finite-time interval. In this regard, two theorems are presented based on Lyapunov–Krasovskii approach and the sufficient conditions are derived as linear matrix inequalities which guarantee the finite-time boundedness of the resulting uncertain closed-loop system. The effectiveness of the proposed method is illustrated by two examples, one numerical and one practical (time-delay Chua's circuit) with simulation results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the delay-dependent robust resilient H ∞ control problem for uncertain singular time-delay system with Markovian jumping parameters. First, a delay-dependent bounded real lemma in terms of linear matrix inequalities is established, which guarantees the nominal Markovian jump singular system to be regular, impulse free and stochastically stable. Then, based on this condition, sufficient conditions in terms of LMIs are given to ensure the existence of the desired robust resilient H ∞ controllers. The uncertainties of the controllers are considered in two cases, that is the additive controller gain uncertainties and the multiplicative controller gain uncertainties. Finally, numerical examples illustrate the applicability of the results proposed in this paper. [ABSTRACT FROM AUTHOR]

We propose a control algorithm for linear objects with a input time-delay in the presence of external disturbances. First, the state predictor and the disturbance predictor are used to synthesize the algorithm. The state predictor performs asymptotic prediction of the state vector, therefore, the closed-loop system contains the state delay. Thus, there exist an upper bound of the delay for which the closed-loop system remains stable. The disturbance predictor is designed under the assumption of the existence of bounded derivatives of the disturbance. Further, the state and disturbance subpredictors are constructed in the form of a serial connection of the corresponding predictors performing multi-step prediction. Sufficient conditions for the stability of the closed-loop system are obtained in the form of feasibility of linear matrix inequalities. We show simulation results that illustrate the effectiveness of the proposed scheme compared to some existing ones. Numerical examples show that the obtained sufficient conditions guarantee the stability of the controller based on the subpredictors with a larger delay than a controller based on predictors. [ABSTRACT FROM AUTHOR]

This paper is concerned with robust stochastic stabilization for positive Markov jump systems with actuator saturation. The considered systems contain interval and polytopic uncertainties, respectively. First, a stochastic co-positive Lyapunov functional is constructed for the systems. By virtue of the presented Lyapunov functional, a new controller design approach is addressed using matrix decomposition technique. Under the designed controller, robust stochastic stabilization of the systems with interval and polytopic uncertainties is achieved, respectively. Furthermore, an effective method for estimating the attraction domain is established by solving an optimization problem. An implemental algorithm is provided based on linear programming to solve the corresponding conditions. Finally, two numerical examples are provided to illustrate the reduced conservatism and effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]

In this draft, we consider the problem of robust extended dissipativity for uncertain discrete-time neural networks (DNNs) with time-varying delays. By constructing appropriate Lyapunov-Krasovskii functional (LKF), sufficient conditions are established to ensure that the considered time-delayed uncertain DNN is extended dissipative. The derived conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the superiority of this result. [ABSTRACT FROM AUTHOR]

We formulate the control design problem for systems with structured uncertainty. The source of disturbances that affect both the input and the output of the system is represented by the same vector-valued signal. The method proposed for the solution of this problem is based on the concept of invariant ellipsoids. The efficiency of the approach is exemplified via application to a model of a fighter aircraft. [ABSTRACT FROM AUTHOR]

Consideration was given to the indeterminate nth order system with l observed coordinates and l controls l < n. With the use of a backstepping-based construction of the observer and quadratic Lyapunov function, designed were continuous or pulse controls under which the system becomes globally asymptotically stable. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic output feedback control problem of discrete-time singularly perturbed systems is considered based on the reduced-order technique. We first show that a proper but not strictly proper dynamic output feedback controller designed for the reduced-order model generally is not a stabilizing compensator for the original system, even though the fast subsystem is stable. To obtain the robustness of the dynamic output feedback controller, an auxiliary system is designed. Based on this, the design of the dynamic output feedback for the reduced-order subsystem is reduced to the simultaneous design of a static output feedback controller for the fast subsystem and a strictly proper dynamic output feedback controller for the auxiliary system, respectively. Based on the obtained results, we confirm that it is possible to generate the robustness for the proposed dynamic output feedback control. Thus, the restriction on the strict properness can be alleviated. Finally, a realistic practical example for the nuclear reactor model is provided to show the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the robust $$H_{\infty }$$ control for a class of uncertain singular time-delay systems via a novel sliding mode observer scheme. Firstly, a particularly non-fragile observer is introduced to estimate the unmeasured states, and a novel integral sliding surface function is presented. Then, a sufficient condition for the admissibility and specified $$H_{\infty }$$ performance of the resultant sliding mode dynamics of the closed-loop systems is derived in terms of linear matrix inequality. At last, the finite-time reachability of the predesigned sliding surface is guaranteed by utilizing the adaptive sliding mode control law from the initial time. An illustrative example is provided to verify the potential and superiority of the method with comparisons. [ABSTRACT FROM AUTHOR]

This paper deals with the robust stabilization of a class of linear parameter varying systems in the continuous control case. Instead of using a state observer or searching for a dynamic output feedback, the considered controller is based on output derivative estimation. This allows the stabilization of the plant with very large parameter variation or uncertainties. The robustness of such controller, for any all-poles single-input/single-output system, is provided for second- and third-order plants. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. The result is a control structure with only one parameter tuned via very simple conditions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of model reduction for neutral-type control system. For a given stable neutral-type control system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in a robust performance but is also translated into a linear lower-dimensional system. Sufficient condition is proposed for the asymptotic stability with an error performance for the error system. Then, the model reduction problem is solved by using the projection approach, which casts the model reduction subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, model reduction with special structures is obtained, i.e., no neutral-type model. A numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed controller design approach. [ABSTRACT FROM AUTHOR]

In this paper, a reliable robust discrete gain scheduling controller is designed based on the linear matrix inequalities (LMIs) and gain scheduling technology for the systems with the input saturation, system uncertainty, external disturbance and actuator failures. By the designed discrete gain scheduling controller, we can use a series of nesting ellipsoid invariant sets to strengthen the disturbance attenuation ability as strong as possible. It means that the innermost invariant ellipsoid set needs to be minimized to strengthen the disturbance attenuation ability. The dynamic performance of the closed-loop system is improved by introducing a parameter. By the Lyapunov approach, the existing conditions for the admissible controller can be formulated in the form of LMIs. The numerical simulation illustrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Traditional underwater vehicles are limited in speed due to dramatic friction drag on the hull. Supercavitating vehicles exploit supercavitation as a means to reduce drag and increase their underwater speed. Compared with fully wetted vehicles, the nonlinearities in modeling of cavitator, fin, and in particular, nonlinear planing force make the control design of supercavitating vehicles more challenging. By combining cascaded design and backstepping approach, this paper reformulates the supercavitating vehicle model into a novel cascade model with two error tracking subsystems. Based on linear matrix inequalities (LMIs) and by introducing the sector conditions of the nonlinear characteristics of planing force, a new finite-time robust $$H_{\infty }$$ control scheme is proposed for the error tracking subsystems which ensures that the closed-loop system is finite-time bounded and the effect of the disturbance input on the controlled output is reduced to a prescribed level. A sufficient condition is presented for the solvability of the design problem, which is further reduced to a feasibility problem of a set of LMIs. Simulations have been conducted for both initial and tracking responses to evaluate the performance and robustness of the proposed $$H_{\infty }$$ controller for all admissible uncertainties and the disturbance inputs. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics analysis and robust control law design for the proposed schematic design of electric unicycles. The schematic design of the proposed unicycle possesses a supportive seat for the rider and is also equipped with a handling rod for maneuvering, similar to a Segway device. First, this paper conducts an analysis and comparison of the dynamics properties and derivation of the nonlinear governing equation for the unicycle. Next, it emphasizes the development of an input-constrained robust controller design for the proposed configuration of the electric unicycle. The issues investigated in this paper include the dynamics property analysis and comparison, nonlinear dynamics derivation, robust control diagram formulation, controller synthesis regarding linear matrix inequalities (LMIs), and time response simulations and discussions. In this control law design via LMIs, the desired performances of: (1) relative stability or decay rate for command tracking capability; (2) disturbance attenuation for robustness against uncertainty parameters; and (3) an accommodation of control effort constraints under the regulation or command tracking of certain initial state condition are investigated and demonstrated using time response simulations of the controlled unicycle dynamics. [ABSTRACT FROM AUTHOR]

This paper considers a problem of attenuation of uncertain stochastic disturbances exciting a linear discrete time-invariant system. The system's abilities to attenuate the external disturbances are quantitatively characterized by its anisotropic norm. The anisotropic control problem is solved for a standard plant with several groups of channels from the external disturbance inputs to the controlled outputs. These channels have different levels of statistic uncertainty measured in terms of the mean anisotropy. The considered technique also allows to design the anisotropic controllers that ensure the closed-loop poles to be placed in some given convex region of the complex plain. [ABSTRACT FROM AUTHOR]

For a double-input single-output system, this paper defines a disturbance attenuation level (called H / γ norm) as the maximum-value L norm of the output under an unknown disturbance with a bounded L norm supplied to the first input and an impulsive disturbance in the form of the product of an unknown vector and the delta function supplied the second input, where the squared L norm of the former disturbance plus the quadratic form of the impulsive disturbance vector does not exceed 1. Weight matrix choice in the H / γ norm yields a trade-off between the attenuation level of the L disturbance and the attenuation level of the impulsive disturbance in corresponding channels. For the uncertain systems with dynamic or parametric uncertainty in the feedback loop, a robust H / γ norm is introduced that includes the robust H and γ norms as special cases. All these characteristics or their upper bounds in the uncertain system are expressed via solutions of linear matrix inequalities. This gives a uniform approach for designing optimal and robust control laws with the H / γ , H and γ performance criteria. [ABSTRACT FROM AUTHOR]

In this paper, a stabilization problem of bilinear control systems is considered. Using the linear matrix inequality technique and quadratic Lyapunov functions, an approach is proposed to the construction of the so-called stabilizability ellipsoid such that the trajectories of the closed-loop system emanating from any point inside this ellipsoid asymptotically tend to the origin. The approach allows for an efficient construction of nonconvex approximations to stabilizability domains of bilinear systems. The results are extended to robust formulations of the problem, where the system matrix is subjected to structured uncertainty. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of the fault detection for switched T-S fuzzy systems with actuator faults. The system faults and unknown disturbances are considered to be in a finite frequency domain. An effective fault detection filter is designed to measure the fault sensitivity and disturbance robustness. By using Parseval's theorem and S-procedure, a new finite frequency method of fault detection for switched T-S fuzzy systems is formulated. Sufficient linear matrix inequalities (LMIs) conditions are proposed to design the fault detection filter, which can guarantee the finite frequency $H_{-}$ and $H_{\infty}$ performance. The effectiveness of the given finite frequency method for switched T-S fuzzy systems is illustrated through two numerical simulation examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of robust state-feedback controllers for uncertain positive Takagi-Sugeno systems with time-delay. The $$\alpha $$ -stabilization by static state-feedback controllers with memory is investigated, taking into account the positivity and the interval uncertainties of the delayed closed-loop system into account. For this, new sufficient $$\alpha $$ -stabilization conditions are established in terms of LMIs. An example illustrates of the proposed approach. [ABSTRACT FROM AUTHOR]

In the problems of estimation and filtering under uncertainty in the regressors, parameters, and covariances of random noise and perturbations, the best possible upper boundary of the proportionality coefficient between the root-mean-square error of estimate or filter and the sum of variances of all random factors was determined. This boundary which was named the level of suppression of random perturbations is characterized in terms of the linear matrix inequalities. The minimax estimate and minimax filter optimizing this index were established. The optimal robust estimate and filter were obtained using additional information about the membership of the covariance matrix in the given convex polyhedron. [ABSTRACT FROM AUTHOR]

This paper considers the problem of robust $H_{\infty}$ control for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. By using the linear matrix inequality (LMI) approach, a sufficient condition is presented for a prescribed uncertain singular system with time-delay to have generalized quadratic stability and $H_{\infty}$ performance. Furthermore, the design methods of state feedback controllers are considered such that the resulting closed-loop system has generalized quadratic stability with $H_{\infty}$ performance. By means of matrix inequalities, sufficient conditions are derived for the existence of memory-less and memorial static state feedback controllers. The controllers are obtained by the solutions of matrix inequalities. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust stabilization and non-fragile robust control for a class of uncertain stochastic nonlinear time-delay systems that satisfy a one-sided Lipschitz condition. The parametric uncertainties are assumed to be real time-varying and norm bounded. Based on the one-sided Lipschitz condition including useful information of the nonlinear part, a new stability criterion for this class of nonlinear systems is provided. A memoryless non-fragile state-feedback controller is designed to guarantee robust stochastic stability of closed-loop systems. The approach of linear matrix inequalities is proposed to solve the robust stability for stochastic nonlinear systems with time-varying delay, and to obtain new delay-dependent sufficient conditions. Numerical examples are given to illustrate the validity and advantages of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the static output stabilization of uncertain continuous Markov jump linear systems with partly known transition probabilities. Uncertainties in system output matrices are addressed in terms of norm-bounded and polytopic formulations. Adopting a new separation technique, sufficient conditions for designing static output controllers are established in terms of linear matrix inequalities. Compared with the existing results, the proposed methods do not impose equality constraints and calculate the null space of output matrices. A numerical example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We consider the robust stabilization problem for linear multivariable systems whose physical parameters may deviate from computed (nominal) in some known bounds, and the control object is subject to non-measurable polyharmonic external disturbances (with unknown amplitudes and frequencies) bounded in power. We pose the problem of synthesizing a controller that guarantees robust stability of the closed-loop system and additionally ensures given errors with respect to controlled variables in the established nominal mode. The solution of this problem is based on the technique of opening the object-controller system with respect to varying object parameters and can be reduced to a standard H-optimization procedure, while the necessary accuracy is achieved by choosing the weight matrix for controlled object variables. We show the solution for a well-known benchmark problem. [ABSTRACT FROM AUTHOR]

This article aims to investigate the problem of robust finite-time output feedback $$ H_\infty $$ control for stochastic jump systems with incomplete transition rates. Firstly, for the nominal stochastic jump systems, the sufficient conditions for the finite-time boundedness and finite-time output feedback stabilization are developed, respectively. Then, a robust finite-time $$ H_\infty $$ output feedback controller is designed by means of linear matrix inequalities. A key point of this work is to relax the special requirement of completely known transition rates to more general form that mixes two cases of completely known and completely unknown transition rates. Finally, a numerical example is given to demonstrate the applicability of the main results. [ABSTRACT FROM AUTHOR]

The stability and stabilisation problems for a series of continuous stochastic singular systems with multiple time-varying delays are studied in this paper. First, a useful lemma is proposed and a delay-distribution-dependent Lyapunov functional is constructed. Then, a novel delay-distribution-dependent condition is given to ensure the unforced stochastic singular systems to be regular and impulse-free. The mean-square exponential stability of the whole system is guaranteed under the proposed lemma. As a result, a suitable feedback controller is designed via strict linear matrix inequality such that the system's stabilisation problem is guaranteed. Finally, numerical examples are illustrated to show the proposed result are less conservative than the existing ones and the potential of such technology. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of network control systems, regarded as a class of large-scale hybrid systems, for ubiquitous computing environment. The problem of robust exponential stabilization for the hybrid systems is addressed, which are composed of impulsive subsystems with time-delay and parameter uncertainties. Using the Lyapunov-Krasovskii functional approach and linear matrix inequality method, an adaptive robust controller is designed to stabilize the uncertain continuous subsystems. Then the delay-dependent exponential stability conditions for the whole hybrid system are derived by analyzing the stability of the subsystems. An example is given to show the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

For linear multivariable systems, we construct discrete output controllers that guarantee a given stability margin radius on the input or output of a control plant. Besides, given control time is also taken into account. We show that solving such problems reduces to a certain specially constructed standard H-optimization problem. A numerical solution has been implemented in MATLAB with the Robust Control Toolbox suite based on the method of linear matrix inequalities (LMI). [ABSTRACT FROM AUTHOR]

In this paper, the robust synchronization for static neural networks with nonlinear coupling and time-varying delay is studied. By constructing the appropriate augmented Lyapunov-Krasovskii functional, utilizing the theory of Kronecker product and the linear matrix inequality technique, we obtain the delay-dependent synchronization conditions which ensure the nonlinear coupled static neural networks with uncertainties in coupling matrices terms robust synchronization. The robust synchronization problem for the nonlinear hybrid coupled static delayed neural networks is first time investigated in this paper. At last, numerical example is provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust exponential stabilization analysis for nonlinear neutral systems with time-varying delays under impulsive control is addressed. Sufficient delay-dependent exponential stabilization results are derived in terms of linear matrix inequalities by constructing suitable Lyapunov-Krasovskii functional. The control gain matrices are designed using impulsive state-feedback control approach. Also, the nonlinear function is assumed to satisfy the sector-bounded condition which includes Lipschitz condition as a special case. Further numerical examples are provided to show the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

In this paper, we exploit the sliding mode control problem for a fluid power electrohydraulic actuator (EHA) system. To characterize the nonlinearity of the friction, the EHA system is modeled as a linear system with a system uncertainty. Practically, it is assumed that the system is also subject to the load disturbance and the external noise. An integral sliding mode controller is proposed to design. The advanced techniques such as the H control and the regional pole placement are employed to derive the optimal feedback gain which can be calculated by solving a necessary and sufficient condition in the form of linear matrix inequality. A sliding mode control law is developed such that the sliding mode reaching law is satisfied. Simulation and comparison results show the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimal trade-off between robustness, in terms of time-delay margin, and performance of the $\mathcal {L}_{1}$ adaptive controller. Although the architectures of the $\mathcal {L}_{1}$ adaptive control theory can be systematically tuned to trade-off performance for robustness, there is no practical methodology as of today for the design of the underlying filter toward obtaining the optimal performance. The only available results in this direction were given in the form of linear matrix inequalities (LMIs), which are numerically tractable but tend to yield conservative results similar to what one would obtain by applying methods from robust control theory. This paper presents design schemes that are based on search for the design parameters of the filter. We consider filters of certain structures to satisfy the design specifications and investigate their properties over the space of the design parameters. To handle uncertain variables in the design specifications, greedy randomized algorithms are adopted to analyze and synthesize the system performance and robustness in the presence of uncertainties. In addition, we compute approximate sets of allowable design parameters in both analytical and numerical ways. Illustrative examples are provided to demonstrate that these methods can achieve the desired performance and robustness specifications with reasonable degree of conservatism. [ABSTRACT FROM AUTHOR]

This paper proposes a TSK-type fuzzy neural network system (TFNN) for identifying and controlling nonlinear control benchmark problem system. It is available for nonlinear dynamic system with uncertainties. The TFNN system can construct and learn its knowledge base from the input–output training data firstly. Thus, a nonlinear system can be represented by several if-then rules with Gaussian membership functions and TSK-type consequent parts. Based on the learned TFNN system, a robust fuzzy controller is proposed, which combines linear matrix inequality-based fuzzy controller and fuzzy sliding model controller. Rigorous proof of asymptotic stability for the closed-loop system is presented via Lyapunov stability theorem. Several examples are presented to illustrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Consideration was given to the problem of robust filtering for the finite-dimensional linear discrete time-invariant system with measured and estimated outputs. The system is exposed to a random disturbance with the imprecisely known probability distribution. In the information-theoretical terms, the stochastic uncertainty of the input disturbance is defined by the functional of mean anisotropy. The error of estimation was quantified by the anisotropy norm. A sufficient condition for an estimator to exist and ensure that the error is less than the given threshold value was derived in the form of a convex inequality on the determinant of a positive definite matrix and two linear matrix inequalities. [ABSTRACT FROM AUTHOR]