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This paper investigates the stability problem of delayed neural networks (DNNs) with time-varying delay. In the stability analysis of DNNs, the stability conditions are usually in form of second-order polynomial functions with respect to the time delay, which are nonlinear matrices inequalities and difficult to deal with. In order to obtain the stability criteria in terms of linear matrices inequalities (LMIs), some quadratic function negative-definiteness lemmas (QFNDLs) are proposed and widely employed. However, the research about QFNDL is still facing two challenges: large conservativeness and difficulty of optimisation. To overcome the challenges, this paper proposes a parameter-dependent quadratic function negative-definiteness lemma (PDQFNDL) to find the negative-definiteness condition. Compared with existing QFNDLs, the proposed lemma has two advantages: (i) Two moving points are introduced and the whole search interval is divided into two parts by an adjustable parameter, which contribute to the less conservativeness of stability criteria. (ii) The search interval of the adjustable parameter is smaller than the existing QFNDLs and the time of optimisation process is decreased. The proposed lemma is utilised to derive the less conservative stability criteria for DNNs based on a suitable Lyapunov–Krasovskii functional (LKF). Finally, the effectiveness and superiority of proposed stability criteria are demonstrated by several numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the framework of dissipativity-based iterative learning control for singular systems (SSs) is established for the first time. Firstly, under the P-type learning algorithm, it has been demonstrated that the dissipative SSs can achieve the accurate tracking for the desired trajectory in a finite time interval. Secondly, a sufficient condition for the SSs to satisfy dissipativity is given by using the linear matrix inequality (LMI) method, and the solvability criterion of the LMI is further presented. Moreover, the relationship between dissipativity and positive realness is revealed. Finally, two examples are given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the paper, the exponential synchronisation for delayed Clifford-valued coupled switched neural networks via static event-triggering rule is studied. Firstly, the drive-response systems for delayed Clifford-valued coupled neural network models are established. So as to avoid the non-commutativity issue of Clifford number multiplication, the original n-dimensional Clifford-valued models are decomposed into $ 2 ^mn $ 2 m n -dimensional real-valued models. On this basis, the error dynamics system is constructed, and then some new sufficient conditions are presented of the exponential synchronisation for the considered neural network models by using Lyapunov–Krasovskii (L-K) functional approach and the technique of linear matrix inequality. Finally, the effectiveness of the results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

A proportional-derivative (PD)-type iterative learning control (ILC) combined with fault-tolerant control (FTC) for a discrete-time batch process with time-varying delays and uncertainties is presented in this paper. The main goals of paper are to drive the considered output profile to the desired reference with the avoidance of possible process faults, delays and uncertainties. First, the nonlinear estimation problem is simplified to the linear one by introducing an appropriate system reparametrisation to deal with the problem of the simultaneous estimation of state and process fault. Second, to solve the problem of time-varying delays and uncertainties, this paper makes use of the two-dimensional (2-D) and repetitive characteristics of batch processes and introduces the state error, tracking error and estimation error to establish the dynamics model of FTILC that is eventually converted into a linear repetitive process model. Then, sufficient conditions based on the Lyapunov–Krasovskii theory and H ∞ methodology are established to ensure the robust stability along the trial in according with linear matrix inequalities (LMIs) for all uncertainties. Finally, this paper manifests the effectiveness of the proposed sufficient conditions by a simulation of injection moulding process. [ABSTRACT FROM AUTHOR]

This paper considers a design problem of adaptive gain robust model-following/tracking controllers for a class of uncertain systems with multiple unknown dead-zone inputs via piecewise Lyapunov functions. The parameters for dead-zone characteristics are assumed to be unknown, and an adaptive dead-zone inverse method is applied so as to reduce the effect for dead-zone non-linearities. Moreover, for the purpose of reducing the effects of matched and mismatched uncertainties, compensation inputs are introduced. The proposed adaptive gain robust model-following/tracking controller can achieve that the tracking error asymptotically converges to zero. In this paper, by using piecewise Lyapunov functions, we show sufficient conditions for the existence of the proposed adaptive gain robust model-following/tracking controller. Finally, an example is given to demonstrate the effectiveness of the proposed controller design method. [ABSTRACT FROM AUTHOR]

This paper presents a new robust convergence condition of iterative learning control with initial state learning (ILC-ISL) for linear multivariable discrete-time systems in the presence of iteration-varying uncertainty. This method is based on linear matrix inequality (LMI) and provides fixed learning gains during time and iteration. Since the convergence of the ILC algorithm may change due to uncertainty in the parameters of a system, and the ILC algorithm is incapable of dealing with iteration-related challenges, it is a major challenge to reject the effect of iteration varying uncertainty. Besides, in the basic ILC algorithm, the initial state is constant in each iteration and consequently always leads to a tracking error. In this paper, first, a convergence condition of the ILC-ISL algorithm is designed based on closed-loop system stability in the iteration domain, and second, a new robust convergence condition is achieved by the LMI approach. Finally, the effectiveness of the proposed robust convergence scheme is evaluated through a numerical example and a mechanical system, respectively. [ABSTRACT FROM AUTHOR]

In this paper, the problem of practical finite-time coordinated path following control of a multi-agent system in an uncertain Euler flow field is studied. The coordinated path following control system is decoupled into a path following sub-system and a coordinated formation sub-system. The uncertain Euler flow field is estimated by constructing an extended state observer. By embedding the extended state observer into the design of the finite-time controllers for both sub-systems, practical finite-time stability of the coordinated path following control system is proved. Simulation results are provided for validating the feasibility and effectiveness of the control method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the $ H_{\infty } $ H ∞ resilient and event-triggered control of singular Markov jump systems against deception attacks. The deception attacks are modelled as a random bounded signal which is governed by a Bernoulli distributed random variable. The event-triggered scheme is adopted to achieve a trade-off between system performance and network resources. Based on the technique of stochastic Lyapunov–Krasovskii functionals and linear matrix inequalities, efficient criteria are developed such that the closed-loop system is stochastically admissible with a certain $ H_{\infty } $ H ∞ performance under deception attacks. Then, the co-design of resilient controller gains and event-triggered rules is provided in terms of a group of feasible LMIs. Finally, two examples are employed to verify the validity of our design. [ABSTRACT FROM AUTHOR]

This paper examines the boundary stabilisation results for time fractional-order reaction-diffusion systems involving with time-varying delays. The main goal is to design the boundary control for the system by proving the well-posedness of the kernel function using the backstepping method. An invertible Volterra integral transformation is used to convert the considered system into a stable target system. Different from the existing results, the stability results for fractional RDEs are discussed in the sense of the Lyapunov–Krasovskii theory and sufficient conditions are derived with the help of the linear matrix inequality (LMI) approach. Finally, to show the application of the results, the proposed conditions are numerically validated over a time fractional-order reaction-diffusion cellular neural network model. [ABSTRACT FROM AUTHOR]

This paper deals with the state estimation problem for nonlinear algebro-differential parameter-varying systems. Sufficient conditions for the existence of the observer which guarantee stability regarding Linear Matrix Inequalities constraints using the Lyapunov stability theory are given. The approach presented includes the proportional and proportional-integral observer as particular cases and allows some robustness concerning uncertainties and modelling errors and its steady state accuracy. A rolling disc model is given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper intends to analyse the disturbance rejection and output tracking control for a class of nonlinear control systems with disturbances. In this connection, we present a method that combines a proportional-integral observer and nonlinear-equivalent-input-disturbance estimator for superior disturbance rejection performance. Specifically, the nonlinear-equivalent-input-disturbance estimator comprises of equivalent-input-disturbance estimator and nonlinear feedback term, which is employed to estimate and reject the disturbances from the nonlinear system. Notably, the proportional-integral loop in the proportional-integral observer reduces the estimation inaccuracy of the nonlinear-equivalent-input-disturbance. Then the estimated disturbance is intertwined into the repetitive control input to compensate it efficiently. In order to obtain the required results, the proposed control system is converted into a two-dimensional modified repetitive control system to describe the learning and control actions. In particular, the proposed controller enables to adjust the gains directly to improve the learning and control performance and as a result, the tracking accuracy increases. Using a general Lyapunov–Krasovskii functional, singular value decomposition technique and linear matrix inequalities approach, a design algorithm for establishing proportional-integral observer and feedback gains is developed for the system under consideration. Finally, simulation results are given to illustrate the developed method's validity and superiority. [ABSTRACT FROM AUTHOR]

This paper is concerned with the input–output finite-time (IO-FT) stabilisation problem for a class of continuous-time periodic piecewise polynomial systems (PPPSs) with immeasurable states and external disturbances via state estimation-based robust reliable controller. Firstly, to reflect the actuality, a parameter uncertainty that exhibits the random nature and the actuator faults with nonlinear character are considered in the addressed PPPSs and the control scheme, respectively. In detail, the randomness of uncertain parameters is portrayed by the stochastic variable and it is presumed to pursue the Bernoulli distributions. Secondly, to estimate the immeasurable states of PPPSs, a periodic piecewise polynomial observer is designed depending on the output of PPPSs. The main intent of this article is to devise a state estimation-based robust reliable controller to ascertain the IO-FT stabilisation of the PPPSs. Moreover, by bridging the Lyapunov stability theory, linear matrix inequality technique and IO-FT stability theory, the required IO-FT stabilisation conditions in the frame of linear matrix inequality are procured for the system under consideration. Eventually, simulation results of the addressed PPPSs are shown in line with the proposed analytical findings, revealing the competence, inherent capability and utility of the devised control protocol. [ABSTRACT FROM AUTHOR]

This paper presents the design of a robust Restricted-Model-Based control providing tools for both stability and performance analysis of a class of Single-Input-Single-Output (SISO) Takagi–Sugeno (T–S) systems. The proposed method is evaluated in terms of induced L 2 -gain (or so-called H ∞ norm) to be robust to disturbances, sensor noises and uncertainties on the premise variables. Unlike the common approaches reported in the literature that consider exact premise variables, this work deals with the problem of unmeasured premises. The main results of this paper illustrate that stability and performance conditions can be evaluated by examining the feasibility of parametrised sets of linear matrix inequalities (LMIs). The proof of stability is based on the non-linear sector approach of the closed loop under Lyapunov conditions, L 2 norm and system transformations. The result is a control structure with only one parameter tuned via simple conditions. The performance and applicability of the proposed approach are illustrated through numerical simulations of an academic example. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the problem of designing locally stabilizing dynamic output feedback controllers and estimate the domain of attraction for discrete-time Takagi-Sugeno (T-S) fuzzy systems. A realistic scenario is assumed where the control signal is subject to saturation, and the premise variables are partially or completely unmeasured, that is, not available for the control law. As a result, the fuzzy output controller can have a different number of fuzzy rules and a different set of membership functions from the T-S model. To obtain locally stabilizable conditions, we propose modeling the variation rate of the membership functions without using upper bounds, a new contribution in the context of output control of discrete-time T-S systems. The design conditions are expressed as linear matrix inequality relaxations based on fuzzy Lyapunov functions using slack variables introduced by Finsler's lemma. Numerical examples illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the set-membership filtering problem is investigated for a class of polytopic uncertain two-dimensional shift-varying systems with delays and sensor saturation. The measurement information is transmitted between the sensors and the filter through a shared communication network. To avoid data congestions, the Round-Robin (R-R) protocol is employed to regulate the data transmission order. This paper aims to design a robust set-membership filter such that the real system states are always contained in the state estimate ellipsoid in the presence of the state delays, the sensor saturation, the parameter uncertainties, the R-R protocol and the unknown-but-bounded external perturbations. By using the mathematical induction, sufficient condition for the existence of the desired robust set-membership filter is given in the form of recursive linear matrix inequalities, and a convex optimisation method is also proposed to determine the optimal state estimation ellipsoid in the trace sense. One numerical example is also given to illustrate effectiveness of the proposed filtering strategy. [ABSTRACT FROM AUTHOR]

This paper addresses the exponential stabilisation of time-varying delay systems by means of Lyapunov–Krasovskii approaches, Bessel–Legendre inequalities and Linear Matrix Inequalities (LMIs). The key aspect of the proposed control synthesis method is that the LMI conditions are proved for the first time to be hierarchical under time-varying delays, that is to say, a progressive conservatism reduction is achieved as long as the degree of Legendre polynomials is increased. To this end, Finsler's lemma has been properly applied to decouple the Lyapunov matrices from the controller gain. Finally, simulation results are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the distributed mixed H 2 / H ∞ fusion filter design problem is investigated for a class of cyber-physical systems subject to non-ideal measurements under Round-Robin protocol. To save the limited communication resources, the Round-Robin protocol is employed to schedule the data transmissions from the sensors to the remote filters. The measurement is imperfect by taking into account the noises, the random saturations, nonlinearity perturbations and packet dropouts. The objective of this study is to propose a desired fusion filtering method that ensures the prescribed performance constraints on both the local and fusion filtering error dynamics. With the aid of Lyapunov function and stochastic analysis technique, a sufficient condition is established to guarantee the mixed H 2 / H ∞ performance index for the local filtering error systems, and then the filter parameter matrices are derived by resorting to the solutions to some matrix inequalities. Subsequently, on the basis of the obtained local state estimates, the proper fusion parameters are acquired by solving a convex optimisation problem. Finally, a numerical example is provided to demonstrate the effectiveness of the designed fusion filter. [ABSTRACT FROM AUTHOR]

This paper studies the problem of dynamic adaptive event-triggered synchronisation control for a class of complex dynamical networks (CDNs) with parameter uncertainty and stochastic network attacks. In order to save communication resources, reduce the driving burden and overcome the conservatism of fixed parameters, an improved event-triggered control strategy is designed. Firstly, a new synchronisation error model with uncertain of internal coupling weights between nodes and stochastic network attacks on actuator is modelled. Secondly, the Bernoulli stochastic distribution process is used to describe the probability of stochastic attacks, and the actuator failure model is adopted to depict actuator failure. By establishing an appropriate Lyapunov function, some sufficient conditions to ensure the asymptotic stability of the synchronisation error system is derived, which reduces conservatism. In addition, the cooperative design of controller and adaptive event-triggered strategy is solved by solving linear matrix inequality. Eventually, two examples are given to illustrate the effectiveness and potential of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper presents an efficient analytical approach for solving the problem of dissipative control in one-sided Lipschitz singular Caputo fractional-order systems subject to nonlinear perturbations. The approach is based on mathematical transformations, and fractional calculus. A state feedback controller is designed to ensure that the closed-loop system is regular, impulse-free, and finite-time bounded with a dissipativity performance index. The results are established using tractable strict linear matrix inequalities (LMIs) without any equality constraint. Two numerical examples are provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider the energy-to-peak filtering issue for a class of linear parameter-varying (LPV) systems with time delays subject to certain communication regulation under which only one sensor is allowed to transmit its measurement data at each transmission instant. The data communication is regulated by the random access protocol (RAP) for the purpose of avoiding data collisions. The main purpose of this paper is to design an LPV filter such that the resultant filtering error system is asymptotically stable and also satisfies the prescribed l 2 - l ∞ performance in the mean square. Taking into account both the LPV nature and the possible gain perturbations, a parameter-dependent resilient filter is constructed according to the plant dynamics and scheduling behaviour of the RAP. The desired filter gain matrices are obtained by solving a set of linear matrix inequalities. Finally, a simulation example is given to validate the effectiveness and correctness of the filter design scheme. [ABSTRACT FROM AUTHOR]

In the paper, we are concerned about the global asymptotic synchronisation for a class of fuzzy master–slave inertial neural networks with time-varying delays. At present, most of the research on the global asymptotic synchronisation of fuzzy master–slave inertial neural networks with time-varying delays adopt the matrix measure method, linear matrix inequality approach and integral inequality method. While in our paper, we attain three criteria to assure the global asymptotic synchronisation between the master system and the slave system by designing three classes of different novel controllers via the maximum-value analysis approach. The controllers designed and the maximum-value method used in this paper are completely novel compared with these in the existing literatures, which enrich and extend the published results. [ABSTRACT FROM AUTHOR]

This paper addresses novel discrete-time H 2 and H ∞ filter designs for polytopic linear parameter-varying (LPV) systems. A less conservative approach is employed to obtain the synthesis conditions, such that the polytopic LPV system state-space representation may have all its matrices subject to time-varying parameters and be solved by an efficient procedure. Parameter-dependent Lyapunov functions are used to derive both H 2 and H ∞ discrete-time filter design conditions resulting in a poly-quadratic approach in terms of linear matrix inequalities. A multi-objective H 2 / H ∞ solution is also provided. The proposed conditions have the advantage of recovering the established poly-quadratic concept as a particular case, which was an unresolved problem until the present paper. Moreover, using the addressed approach, it is possible to obtain improved quadratic H 2 and H ∞ filters. Numerical examples illustrate the proposed design methods applicability as an observer to estimate LPV system states and its performance in comparison with other approaches. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of local passivity and local feedback passivation of smooth discrete-time nonlinear systems by considering their piecewise affine approximations. Sufficient conditions are derived for local passivity and local feedback passivity. These results are then extended to systems that operate over Gilbert-Elliott type communication channels. One of the main features of the approach presented in this paper is that it allows us to design the controller by solving a few linear matrix inequalities (LMIs) that are subject to certain constraints. As a special case, results for feedback passivity of piecewise affine systems over a lossy channel are also derived. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of finite time dissipativity-based reliable control for a time-varying system with linear fractional uncertainty (LFU) and time delay. An actuator fault model consisting of both linear and nonlinear faults is considered during the time-varying control process. By implementing an augmented time-varying Lyapunov functional and using the Wirtinger-type integral inequality, delay-dependent finite time dissipative conditions are established in forms of derivative linear matrix inequalities (DLMIs), which can guarantee the closed-loop system is finite time dissipative for all admissible uncertainties. Then, the DLMIs are transformed into a series of recursive linear matrix inequalities (RLMIs) based on the discretization method. And an algorithm is given to solve the RLMIs to obtain the state feedback gain. Simulation results demonstrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper proposes a new adaptive gain robust model-following/tracking controller for a class of uncertain linear systems. The proposed adaptive gain robust controller is composed of state feedback laws with fixed gains, feedfoward inputs for the reference model and nonlinear compensation inputs with adjustable time-varying parameters. Moreover, the proposed control strategy can achieve good transient performance and avoid the excessive control input by means of the design parameter. In this paper, linear matrix inequality-based sufficient conditions for the existence of the proposed adaptive gain controller are given, and two design strategies are presented. Finally, simple illustrative examples are included to show the effectiveness of the proposed adaptive gain robust controller. [ABSTRACT FROM AUTHOR]

This paper studies the robust static output feedback control of discrete-time Markov jump systems considering that the mode of operation cannot be directly measured. It is assumed that the only available information concerning the main jump process comes from a detector, so that the jump and detector processes can be modelled as a hidden Markov model. Initially, it is considered that the system's dynamic matrix is subject to parametric uncertainties. By assuming a full row rank condition for the output matrix and employing a clusterisation technique for the state space of the hidden Markov model, it is derived a set of linear matrix inequalities (LMIs) that guarantees robust stability in the mean-square sense of the closed-loop system, as well as a bound on its H 2 norm. It is also shown that this design technique is linked to the bounded real lemma, so that a new set of LMIs conditions can be obtained for the 'pure' H ∞ control problem, which can be extended to cover the robust polytopic case. The paper is concluded with an illustrative example. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of distributed fusion over sensor networks with probabilistic constraints and stochastic perturbations. In order to save the bandwidth resources, a new event-triggering mechanism (ETM), called torus-event-triggering mechanism (TETM), is utilised for data transmission. Compared with the traditional ETMs, the TETM has two thresholds, which will not only discard the sampling data smaller than the lower threshold but also hold back the packet larger than the upper threshold. The main purpose of this paper is to design a time-varying distributed fusion filter such that: (1) the probability of the filtering error falling in a given ellipsoid domain is greater than a specified value and (2) the ellipsoidal set is minimised in the sense of matrix norm at each time point. To achieve the above-mentioned purpose, sufficient conditions are given to obtain the global fusion with the help of the recursive linear matrix inequality technique. The desired local filter parameters are then computed by solving an optimisation problem with some inequality constraints. Finally, a numerical simulation is given to illustrate the effectiveness and applicability of the proposed distributed fusion strategy. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the semi-global asymptotic stabilisation of fractional-order (FO) linear systems subject to actuator saturation by output feedback. To solve the problem, a family of observer-based linear output feedback laws, parameterised in a positive scalar, is proposed by means of the low gain feedback design technique. The design applies to FO linear systems that are stabilisable and detectable, but not exponentially unstable. For such an FO system under the proposed observer-based linear low gain output feedback, the peak value of the control input for a given initial condition can be made arbitrarily small to avoid actuator saturation by decreasing the value of the parameter towards zero and thus semi-global asymptotic stabilisation is achieved. To obtain these results, we establish the properties of low gain feedback, derive asymptotic expansions and the bounds of high-order derivatives of the Mittag-Leffler (ML) functions to estimate the state responses of FO linear systems, and explicitly construct a Hermitian matrix to satisfy a linear matrix inequality (LMI) stability condition for FO linear systems. The results in this paper extend the corresponding results for integer-order (IO) linear systems. [ABSTRACT FROM AUTHOR]

This paper addresses a non-fragile robust model predictive control design for a class of continuous-time uncertain systems with multiple state-delay and constrained control signals. The parameters of the system and the control gain are assumed to have perturbation in the additive form. The Lyapunov–Krasovskii functional approach is employed to derive sufficient conditions for determining a non-fragile robust state-feedback controller for all admissible uncertainties by minimising the upper bound of the defined quadratic cost function with respect to some linear matrix inequalities (LMIs). An additional inequality condition is imposed to address the constraint associated with the control signals. Numerical simulations are provided to assess the performance of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper investigates the stability for a class of distributed-order nonlinear systems via event-triggered control method. First of all, an inequality of the solution is established for distributed-order nonlinear inequality systems by employing Laplace transform. And then, by designing an appropriate state feedback controller and event-triggered strategy, and using Lyapunov stability theory and matrix inequality technique, a sufficient condition to ensure the asymptotic stability of the considered distributed-order nonlinear systems is obtained in the form of linear matrix inequality. Moreover, a criterion to exclude Zeno behaviour in event-triggered strategy is provided. Finally, the feasibility and effectiveness of the proposed method are verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, the mixed H 2 / H ∞ guaranteed cost for continuous-time linear parameter-varying (LPV) systems is proposed. In addition, the gain scheduling (GS) strategy and the state derivative feedback (SDF) were considered. The time-varying parameter is assumed to be available for online measurement, and the conditions are based on linear matrix inequalities (LMIs). To improve the behaviour of the system, the D -stability is used. Examples show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and a mixed H 2 / H ∞ guaranteed cost minimisation. [ABSTRACT FROM AUTHOR]

This paper investigates the mixedH∞and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weightedH∞and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixedH∞and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given. [ABSTRACT FROM PUBLISHER]

In this paper, the fault detection problem is investigated for a class of discrete-time piecewise linear systems with external disturbances and infinite distributed time-delays. As a modelling framework, piecewise linear system often arise when piecewise linear components are encountered, such as dead-zone, saturation, relays and hysteresis. The time-delays are assumed to be infinitely distributed in the discrete-time domain. The aim of this paper is to detect the possible faults and to estimate the system state. For this purpose, firstly, stability analysis is given based on a piecewise smooth Lyapunov function. Afterward, an appropriate approach of fault detection and filter design problem is provided to achieve a satisfactory balance between the disturbances attenuation level γ and the sensitivity to the fault for piecewise linear systems. As a consequence, a sufficient condition is obtained in terms of the linear matrix inequalities such that, for all admissible infinite distributed time-delays and external disturbances, the system is guaranteed to be asymptotically stable and the residual is guaranteed to satisfyH∞filtering performance and fault detection performance. At last, a simulation example is provided to demonstrate the applicability and effectiveness of the fault detection filtering scheme proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the extended dissipative filter design problems for continuous-time fuzzy systems with time-varying delays under imperfect premise variables based on a unified performance index−extended dissipative. Attention is focused on solving theH∞,L2−L∞, passive and dissipative filtering problems for fuzzy systems with time-varying delays under this unified framework. Based on the unified performance index, a new delay-dependent filter design approach in terms of linear matrix inequalities is obtained by employing Lyapunov–Krasovskii functional method together with a novel efficient integral inequality. The designed filter can guarantee the filtering error system satisfy the prescribedH∞,L2−L∞, passive and dissipative performance by tuning the weighting matrices in the conditions. Moreover, in this paper, the fuzzy filter does not need to share the same membership function with fuzzy model, which can enhance design flexibility and robust property of the fuzzy filter system. Finally, two examples are provided to illustrate the effectiveness and significant improvement of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time bounded control for uncertain semi-Markovian jump neural networks with mixed delays which include distributed leakage delay (DLD) and mixed time-varying delays is considered. The system not only contains semi-Markovian jump, linear fractional uncertainties (LFUs), mixed time-varying delays but also includes distributed time delays in the leakage term which is not yet investigated in existing papers. Firstly, uncertainty parameters in the systems are solved by LFU based on the new model. Secondly, a novel augmented Lyapunov–Krasovskii functional (LKF) which involves more information about time-varying delays is constructed. Moreover, latest integral inequalities and time-delays division method are used to estimate the derivative of proposed LKFs. Thirdly, in the framework of uncertainty, semi-Markovian jump, DLD, mixed delays and external disturbance, a full-order state estimator is constructed such that the error dynamic system is finite-time bounded under the condition of given linear matrix inequalities. Finally, usefulness and advantages of the obtained results are verified by three numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fault detection observer design for discrete spatially interconnected time-delay systems (SITSs) in finite frequency range. Firstly, a delay-dependent generalised Kalman–Yakubivich–Popov (GKYP) lemma for SITSs is proposed. Then, by the giving GKYP lemma, a distributed fault detection observer design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates H ∞ event-triggered model predictive control (MPC) problem for switched systems. In network transmission processes, two problems (including limited resources and denial of service (DoS) attacks) profoundly affect the usability of control systems. Especially, DoS attacks that occur in feedback channel can make the systems open-loop. In this regard, a novel memory-based anti-attack strategy is presented, which is implemented by adding a cache function to network controllers. An event-triggering mechanism is adopted to improve network resource utilisation and reduce the probability of transmission data being attacked. MPC technology is employed for network controllers, which optimises the control input and state by minimising an upper bound of a quadratic cost function. Then, closed-loop switched system is established, and the coupling relationship between switching and attacking is clearly discussed. Based on average dwell time approach, H ∞ performance is analysed. The co-design of MPC controllers and event-triggering matrices are given by solving linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the feasibility. [ABSTRACT FROM AUTHOR]

This paper studies the problem of the stochastic admissibility for singular Markovian jump systems with time-varying delay. By introducing two exponential parameters, a new version of reciprocally convex inequality named exponential type reciprocally convex inequality is proposed, which covers some existing results as its special cases. Based on the second-order B-L inequality, a novel delay-product-type functional is proposed to fully capture the information among system states and time-varying delay. Based on the two improved techniques, a less conservative admissibility condition is obtained in terms of linear matrix inequalities. Two examples are introduced to illustrate the effectiveness of the proposed result. [ABSTRACT FROM AUTHOR]

This paper derives the bounded real lemma corresponding to H ∞ norm of the singular fractional-order system (SFOS). The H ∞ bounded real lemma established for both cases of 0 < α < 1 and 1 < α < 2 has no conservatism and it turns the original complex computation of H ∞ norm into linear matrix inequality (LMI) problem, which can be performed in a computationally efficient fashion. In addition, it can test the system stability automatically, which is critical for system analysis. From this advantage, the synthesis problem of H ∞ control for the SFOS is addressed in the form of LMI. The simulation study is performed to validate the effectiveness and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper focuses on the structural stability and stabilisation of the continuous-discrete fractional-order two-dimensional Fornasini-Marchesini first model. The sufficient and necessary stability conditions are given in polynomial form at first. Secondly, to make the problem solvable, based on the property of Kronecker product and the Generalized–Kalman–Yakubovich–Popov Lemma, the new sufficient and necessary stability conditions are established in the form of linear matrix inequalities. Thirdly, with the help of the Projection Lemma, the stabilisation conditions are obtained after introducing a state feedback controller, which can be solved with an iterative linear matrix inequality algorithm. In the end, the effectiveness of the proposed results is verified by two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the admissibility analysis and controller design issues for a class of nonlinear descriptor systems described by the T–S descriptor fuzzy model with partially unknown membership functions are discussed. New sufficient conditions are first given to ensure the admissibility of such fuzzy descriptor systems. To fully utilise the information of membership functions, the known and unknown parts of membership functions are handled by staircase functions and the bounds of the unknown part, respectively. Different from the traditional parallel distribution compensation (PDC) method, the state-feedback controller design condition is given under an imperfect premise matching method via linear matrix inequalities (LMIs). Some examples are given to show the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper analyses the stability problem of linear systems with interval time-varying delay. In regard to the delay, it has the lower and upper bounds and its derivative is unknown or itself is not differentiable. First of all, it is the first time that the delay-related triple integral terms are used to construct the augmented Lyapunov–Krasovskii functional (LKF) and the delay-related integral quadratic terms are estimated by the third-order free-matrix-based integral inequalities (TFIIs). Then, based on the same LKF and same TFIIs and by introducing two sets of state vectors, the derivative of the LKF is presented as the quadratic and quintic polynomials about the delay respectively. Next, for the quadratic and quintic polynomials, new negative definite conditions (NDCs) are provided to form the linear matrix inequality (LMI) conditions. Finally, the advantages of these two criteria are checked through some classical numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a novel method to design a robust L 1 observer and its circuit implementation for the problems of fault diagnosis and state estimation in nonlinear systems expressed by Takagi–Sugeno models. The proposed observer is able to estimate states of system, process/actuator and sensor faults at the same time, and also has a high resistance to disturbances. The sufficient conditions to design the proposed observer such that ensuring the stability of the system based on to the Lyapunov theory and minimising an L 1 performance index are given by Linear Matrix Inequality (LMI) optimisation problems. Moreover, the circuit implementation of the Van der Pol system and the proposed observer scheme is provided in detail. Also, the simulation results validate the effectiveness of the proposed L 1 observer and fault diagnosis approach. [ABSTRACT FROM AUTHOR]

In this paper, the reduced-order H ∞ filtering problem for discrete-time singular systems under fading channels is studied. Our aim is to design a reduced-order filter to ensure the filtering error system with fading measurements is stochastically admissible and meets the given performance index. And the designed method is less conservative. However, the standard linear matrix inequality (LMI) cannot be obtained due to the nonlinear terms in decoupling. For this purpose, a new LMI is obtained by using new decoupling method. Finally, numerical example and electrical circuit example are given to clearly illustrate that the proposed method is less conservative than that of the existing method. [ABSTRACT FROM AUTHOR]

This paper investigates robust sliding mode control (SMC) for discrete singular systems which include time-varying delays, parameter uncertainties and nonlinear perturbations. An appropriate discrete sliding surface function is constructed such that the corresponding sliding mode dynamics are gained. By using some free-weighting matrices, a linear matrix inequality constraint is established to make sure that the closed-loop system is regular, causal and stable. Furthermore, in consideration of the improved discrete reaching condition, an SMC law is synthesised for reaching motion and the chattering can be weakened, while few existing papers focus on how to employ it to study the SMC problem for the discrete singular systems with time-varying delays. At last, the designed law is tested through an example. [ABSTRACT FROM PUBLISHER]

In this paper, the practical mean-square scaled-consensus problem of multiagent systems is studied. Higher-order general linear dynamics is investigated, where all agents are subject to faults or denial of service attacks (DoS). The considered network comprises agents taking quantised states under undirected communication channels. Different from the existing works, no strict conditions have been imposed on the eigenvalues of the agents' state matrix. First, we propose a distributed scaled-consensus protocol that utilises a probabilistic quantisation algorithm. Second, scaled-disagreement analysis is provided via mean-square stability methodology. Finally, sufficient conditions in terms of linear matrix inequalities are presented in order to obtain scaled-consensus gain for both leaderless and leader–follower cases. The presented theoretical results are examined through two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time observer-based control for linear fractional-order systems with interval time-varying delay is studied. The delay is assumed to vary within an interval with known lower and upper bounds. A new proposition on estimating Caputo derivatives of quadratic functions is given. Based on the proposed result, delay-dependent sufficient conditions for finite-time stability and for designing state feedback controllers and observer gains for observer-based control problem are established in terms of a tractable linear matrix inequality and Mittag–Leffler function. A numerical example with simulation is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of observer-based reliable passive control for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-delay and actuator faults. By employing Lyapunov stability theory, fault treatment method and linear matrix inequalities (LMIs), a sufficient condition on the existence of an observer-based reliable passive controller is given. Further, the LMI conditions are proposed for the observer-based reliable passive controller design. The gain of reliable controller and observer can be obtained by solving the proposed LMIs. Using the reliable passive controller, the closed-loop system is not only internally stable but also strictly passive even though some actuator components fail and system state fails to be measured completely. Finally, a truck-trailer system example is given to verify the effectiveness and advantages of the designed approach. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic output feedback robust model predictive control for system with polytopic model uncertainty. Earlier researches on this topic utilise iterative methods to solve the non-convex optimisation problem which are computationally demanding. In order to reduce the computational burden, we explore a new approach in this paper, where, by utilising some proper matrix transformations, a computationally more efficient but conservative convex optimisation problem is formulated which can be solved in terms of linear matrix inequalities. Furthermore, we try to reduce the conservativeness by introducing a nonsingular matrix as a degree of freedom. The recursive feasibility and the convergence of the augmented state to the equilibrium point are guaranteed. The effectiveness of the proposed approach is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]