Robust stability and H∞ control for nonlinear discrete‐time switched systems with interval time‐varying delay

This paper considers the problems of the robust stability analysis and H_∞ controller synthesis for uncertain discrete‐time switched systems with interval time‐varying delay and nonlinear disturbances. Based on the system transformation and by introducing a switched Lyapunov‐Krasovskii functional, the novel sufficient conditions, which guarantee that the uncertain discrete‐time switched system is robust asymptotically stable are obtained in terms of linear matrix inequalities. Then, the robust H_∞ control synthesis via switched state feedback is studied for a class of discrete‐time switched systems with uncertainties and nonlinear disturbances. We designed a switched state feedback controller to stabilize asymptotically discrete‐time switched systems with interval time‐varying delay and H_∞ disturbance attenuation level based on matrix inequality conditions. Examples are provided to illustrate the advantage and effectiveness of the proposed method.     

Nonfragile H∞ output tracking control for uncertain singular Markovian jump delay systems with network‐induced delays and data packet dropouts

This article deals with the problem of nonfragile H_∞ output tracking control for a kind of singular Markovian jump systems with time‐varying delays, parameter uncertainties, network‐induced signal transmission delays, and data packet dropouts. The main objective is to design mode‐dependent state‐feedback controller under controller gain perturbations and bounded modes transition rates such that the output of the closed‐loop networked control system tracks the output of a given reference system with the required H_∞ output tracking performance. By constructing a more multiple stochastic Lyapunov–Krasovskii functional, the novel mode‐dependent and delay‐dependent conditions are obtained to guarantee the augmented output tracking closed‐loop system is not only stochastically admissible but also satisfies a prescribed H_∞‐norm level for all signal transmission delays, data packet dropouts, and admissible uncertainties. Then, the desired state‐feedback controller parameters are determined by solving a set of strict linear matrix inequalities. A simple production system example and two numerical examples are used to verify the effectiveness and usefulness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 396–411, 2016     

Dissipative analysis for discrete‐time systems via fault‐tolerant control against actuator failures

This article investigates the problem of robust dissipative fault‐tolerant control for discrete‐time systems with actuator failures. Based on the Lyapunov technique and linear matrix inequality (LMI) approach, a set of delay‐dependent sufficient conditions is developed for achieving the required result. A design scheme for the state‐feedback reliable dissipative controller is established in terms LMIs which can guarantee the asymptotic stability and dissipativity of the resulting closed‐loop system with actuator failures. In addition, the proposed controller not only stabilize the fault‐free system but also to guarantee an acceptable performance of the faulty system. Also as special cases, robust H_∞ control, passivity control, and mixed H_∞ and passivity control with the prescribed performances under given constraints can be obtained for the considered systems. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault‐tolerant control technique. © 2016 Wiley Periodicals, Inc. Complexity 21: 579–592, 2016     

Finite‐time synchronization of a class of N‐coupled complex partial differential systems with time‐varying delay

This study examines finite‐time synchronization for a class of N‐coupled complex partial differential systems (PDSs) with time‐varying delay. The problem of finite‐time synchronization for coupled drive‐response PDSs with time‐varying delay is similarly considered. The synchronization error dynamic of the PDSs is defined in the q‐dimensional spatial domain. We construct a feedback controller to achieve finite‐time synchronization. Sufficient conditions are derived by using the Lyapunov‐Krasoviskii stability approach and inequalities technology to ensure that the proposed networks achieve synchronization in finite time. The proposed systems demonstrate extensive application. Finally, an example is used to verify the theoretical results.     

Robust reliable L2 – L∞ control for continuous‐time systems with nonlinear actuator failures

This article examines the reliable L₂ – L_∞ control design problem for a class of continuous‐time linear systems subject to external disturbances and mixed actuator failures via input delay approach. Also, due to the occurrence of nonlinear circumstances in the control input, a more generalized and practical actuator fault model containing both linear and nonlinear terms is constructed to the addressed control system. Our attention is focused on the design of the robust state feedback reliable sampled‐data controller that guarantees the robust asymptotic stability of the resulting closed‐loop system with an L₂ – L_∞ prescribed performance level γ > 0, for all the possible actuator failure cases. For this purpose, by constructing an appropriate Lyapunov–Krasovskii functional (LKF) and utilizing few integral inequality techniques, some novel sufficient stabilization conditions in terms of linear matrix inequalities (LMIs) are established for the considered system. Moreover, the established stabilizability conditions pave the way for designing the robust reliable sampled‐data controller as the solution to a set of LMIs. Finally, as an example, a wheeled mobile robot trailer model is considered to illustrate the effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 309–319, 2016     

Robust partially mode‐dependent H∞ filtering for discrete‐time nonhomogeneous Markovian jump neural networks with additive gain perturbations

This paper studies the robust partially mode‐dependent H_∞ filtering for nonhomogeneous Markovian jump neural networks with additive gain perturbations. The discrete time‐varying jump transition probability matrix is considered to be a polytope set. A partially mode‐dependent filter with additive gain perturbations is constructed to increase the robustness of the filter, which is subjects to H_∞ performance index. Based on the Lyapunov function approach, sufficient conditions are established such that the filtering error system is robustly stochastically stable. The efficiency of the new technique is illustrated by an illustrative example and a biological network example.     

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

The problem of H_∞ robust control based on event‐triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event‐triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H_∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean‐square admissible and has a prescribed H_∞ performance γ. Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method.     

Reliable gain‐scheduled control design for networked control systems

In this article, the problem of reliable gain‐scheduled H_∞ performance optimization and controller design for a class of discrete‐time networked control system (NCS) is discussed. The main aim of this work is to design a gain‐scheduled controller, which consists of not only the constant parameters but also the time‐varying parameter such that NCS is asymptotically stable. In particular, the proposed gain‐scheduled controller is not only based on fixed gains but also the measured time‐varying parameter. Further, the result is extended to obtain a robust reliable gain‐scheduled H_∞ control by considering both unknown disturbances and linear fractional transformation parametric uncertainties in the system model. By constructing a parameter‐dependent Lyapunov–Krasovskii functional, a new set of sufficient conditions are obtained in terms of linear matrix inequalities (LMIs). The existence conditions for controllers are formulated in the form of LMIs, and the controller design is cast into a convex optimization problem subject to LMI constraints. Finally, a numerical example based on a station‐keeping satellite system is given to demonstrate the effectiveness and applicability of the proposed reliable control law. © 2014 Wiley Periodicals, Inc. Complexity 21: 214–228, 2015     

Dissipative sampled‐data control of uncertain nonlinear systems with time‐varying delays

This article investigates the delay‐dependent robust dissipative sampled‐data control problem for a class of uncertain nonlinear systems with both differentiable and non‐differentiable time‐varying delays. The main purpose of this article is to design a retarded robust control law such that the resulting closed‐loop system is strictly (Q, S, R)‐dissipative. By introducing a suitable Lyapunov–Krasovskii functional and using free weighting matrix approach, some sufficient conditions for the solvability of the addressed problem are derived in terms of linear matrix inequalities. From the obtained dissipative result, we deduce four cases namely, H_∞ performance, passivity performance, mixed H_∞, and passivity performance and sector bounded performance of the considered system. From the obtained result, it is concluded that based on the passivity performance it is possible to obtain the controller with less control effort, and also the minimum H_∞ performance and the maximum allowable delay for achieving stabilization conditions can be obtained via the mixed H_∞ and passivity control law. Finally, simulation studies based on aircraft control system are performed to verify the effectiveness of the proposed strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 142–154, 2016     

H∞ control of a class of networked control systems with time delay and packet dropout

This paper studies the H-infinity control issue for a class of networked control systems (NCSs) with time delay and packet dropout. The state feedback closed-loop NCS is modeled as a discrete-time switched system. Through using a Lyapunov function, a sufficient condition is obtained, under which the system is exponential stability with a desired H-infinity disturbance attenuation level. The designed H-infinity controller is obtained by solving a set of linear matrix inequalities. An illustrative example is presented to demonstrate the effectiveness of the proposed method.     

Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria

This study concerns with the robust H _∞ synchronization problem for a class of nonlinear feedback control systems, which are subject to a vector-valued periodic nonlinearity in the feedback path. Under such synchronization configuration, the master system is assumed to be subject to an energy bounded input disturbance, and the slave one is under control. Sufficient conditions for controller design are proposed in terms of linear matrix inequalities by respectively utilizing the output feedback control and the dynamic output control strategies, such that the master system robustly synchronizes the slave one with a guaranteed H _∞ performance. The derived methods can be applied to the robust H _∞ synchronization of many practical systems, and effectiveness of the obtained results are demonstrated through a concrete example of phase-locked loops (PLL).     

Exponential stabilization and L2‐gain for uncertain switched nonlinear systems with interval time‐varying delay

This paper is concerned with the exponential stabilization and L₂‐gain for a class of uncertain switched nonlinear systems with interval time‐varying delay. Based on Lyapunov–Krasovskii functional method, novel delay‐dependent sufficient conditions of exponential stabilization for a class of uncertain switched nonlinear delay systems are developed under an average dwell time scheme. Then, novel criteria to ensure the exponential stabilization with weighted L₂‐gain performance for a class of uncertain switched nonlinear delay systems are established. Furthermore, an effective method is proposed for the designing of a stabilizing feedback controller with L₂‐gain performance. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Mode Dependent H∞ Filtering for Discrete-Time Networked Systems with Random Measurement Missing and Delays

The article investigates the H_∞ filtering problem for a class of discrete-time networked systems with random measurement losses and delays. Markov chain is used here to model measurement losses and delays in a unified framework. Based on the mode-dependent Lyapunov function approach, the necessary and sufficient conditions are derived to guarantee the exponential stability with a prescribed H_∞ disturbance attenuation performance for the filtering error system. By using a novel design scheme, the explicit expressions of mode dependent filter parameters are given in the form of linear matrix inequalities (LMIs) which can be readily solved by using the LMI TOOLBOX in MATLAB. At last, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays

In this paper, we aim to study the robust global exponential synchronization problem for a general class of Lur’e chaotic systems subject to time delays and impulsive disturbances. Furthermore, we also provide an estimation of the maximum Lyapunov exponent. By using the Lyapunov function method and linear matrix inequality (LMI) technique, sufficient conditions for the robust global exponential synchronization and estimation of its maximum Lyapunov exponent are obtained for the class of Lur’e chaotic systems with and without time delays, respectively. Furthermore, by applying the M-matrix theory, some of these sufficient conditions are shown to be expressible in forms of fairly simple algebraic conditions. For illustration, several examples are solved by using the sufficient conditions obtained.     

Robust H∞ output dynamic observer-based control of uncertain time-delay systems

In this paper, the robustness and H_∞ control problems of output dynamic observer-based control for a class of uncertain linear systems with time delay are considered. Under no disturbance input, the asymptotic stabilization for uncertain time-delay systems will be guaranteed. Linear matrix inequality (LMI) optimization approach is used to design three classes of the H_∞ output dynamic controls. Based on the results of this paper, the constraint of matrix equality is not necessary for designing the observer-based controls.     

Fuzzy delayed output feedback synchronization for time-delayed chaotic systems

In this paper, we propose a new fuzzy delayed output feedback synchronization (FDOFS) method for time-delayed chaotic systems. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the FDOFS controller is designed and an analytic expression of the controller is shown. The proposed controller can guarantee asymptotical synchronization of both drive and response systems. The FDOFS controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed FDOFS method.     

On the computation of the infimum in H∞‐optimization

In this paper, a new method for the computation of the infimum for a large class of continuous‐time H_∞ optimal control problem by state feedback is presented. The main ingredients of the new method include three generalized eigenvalue problems whose coefficient matrices are from a condensed form of the given system. This condensed form is computed using only orthogonal transformations which can be implemented via a numerically stable way. The superiority of the new method over the existing one given in Chen (H_∞ Control and its Applications, Chapter 5. Springer: Berlin, 1997) is verified by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd.     

Delay-dependent robust control for uncertain discrete-time singular systems with time-delays

The robust memoryless state feedback H_∞ control problem for uncertain time-delay discrete-time singular systems is discussed. Under a series of equivalent transformation, the equivalence of this problem and the robust state feedback H_∞ control problem for standard state-space uncertain time-delay discrete-time systems is presented. In terms of matrix inequality, the delay-dependent sufficient condition for the solution of this problem is given, the design method of the memoryless state feedback controller and the controller are also given.     

On pth moment stabilization of hybrid systems by discrete-time feedback control

Since Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) by feedback controls based on discrete-time state observations in 2013, many authors have further studied and developed it. However, so far no work on the pth moment stabilization has been reported. This paper is to investigate how to stabilize a given unstable hybrid SDE by feedback controls based on discrete-time state observations, in the sense of H_∞, asymptotic and exponential stability in pth moment for all p > 1. The main techniques used are constructions of the Lyapunov functionals and generalizations of inequalities.     

Second-order nonsmooth optimization for <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> synthesis

The standard way to compute H _∞ feedback controllers uses algebraic Riccati equations and is therefore of limited applicability. Here we present a new approach to the H _∞ output feedback control design problem, which is based on nonlinear and nonsmooth mathematical programming techniques. Our approach avoids the use of Lyapunov variables, and is therefore flexible in many practical situations.