Exponential H∞ synchronization for discrete‐time chaotic neural networks with time delays and stochastic perturbations via output feedback control

This paper investigates the problem of exponential H_∞ synchronization of discrete‐time chaotic neural networks with time delays and stochastic perturbations. First, by using the Lyapunov‐Krasovskii (Lyapunov) functional and output feedback controller, we establish the H_∞ performance of exponential synchronization in the mean square of master‐slave systems, which is analyzed using a matrix inequality approach. Second, the parameters of a desired output feedback controller can be achieved by solving a linear matrix inequality. Finally, 2 simulated examples are presented to show the effectiveness of the theoretical results.     

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.     

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     

Improved H∞ performance analysis of uncertain Markovian jump systems with overlapping time‐varying delays

In this article, we study the problem of robust H_∞ performance analysis for a class of uncertain Markovian jump systems with mixed overlapping delays. Our aim is to present a new delay‐dependent approach such that the resulting closed‐loop system is stochastically stable and satisfies a prescribed H_∞ performance level χ. The jumping parameters are modeled as a continuous‐time, finite‐state Markov chain. By constructing new Lyapunov‐Krasovskii functionals, some novel sufficient conditions are derived to guarantee the stochastic stability of the equilibrium point in the mean‐square. Numerical examples show that the obtained results in this article is less conservative and more effective. The results are also compared with the existing results to show its conservativeness. © 2016 Wiley Periodicals, Inc. Complexity 21: 460–477, 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     

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     

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.     

Delay‐dependent robust reliable control for uncertain switched neutral systems

This article investigates the robust reliable control problem for a class of uncertain switched neutral systems with mixed interval time‐varying delays. The system under study involves state time‐delay, parameter uncertainties and possible actuator failures. In particular, the parameter uncertainties is assumed to satisfy linear fractional transformation formulation and the involved state delay are assumed to be randomly time varying which is modeled by introducing Bernoulli distributed sequences. The main objective of this article is to obtain robust reliable feedback controller design to achieve the exponential stability of the closed‐loop system in the presence of for all admissible parameter uncertainties. The proposed results not only applicable for the normal operating case of the system, but also in the presence of certain actuator failures. By constructing an appropriate Lyapunov–Krasovskii functional, a new set of criteria is derived for ensuring the robust exponential stability of the closed‐loop switched neutral system. More precisely, zero inequality approach, Wirtinger's based inequality, convex combination technique and average dwell time approach are used to simplify the derivation in the main results. Finally, numerical examples with simulation result are given to illustrate the effectiveness and applicability of the proposed design approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–237, 2016     

RBF‐based discrete sliding mode control for robust tracking of uncertain time‐delay systems with input nonlinearity

In this article, a control scheme combining radial basis function neural network and discrete sliding mode control method is proposed for robust tracking and model following of uncertain time‐delay systems with input nonlinearity. The proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties, and external disturbances. The salient features of the proposed controller include no requirement of a priori knowledge of the upper bound of uncertainties and the elimination of chattering phenomenon and reaching phase. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 194–201, 2016     

Stochastic stabilization of networked control systems with combined stochastic distributed processes

The stochastic stability problem of networked control systems (NCSs) with random time delays and packet dropouts is investigated in this paper. The mathematical NCS model is developed as a stochastic discrete‐time jump system with combined integrated stochastic parameters characterized by two identically independently distributed processes, which accommodate the abrupt variations of network uncertainties within an integrated frame. The effective instant is introduced to establish the relationship between the destabilizing transmission factors and stability of NCSs. The stabilizing state feedback controller gain that depends not only on the delay modes but also on the dropouts modes is obtained in terms of the linear matrix inequalities formulation via the Schur complement theory. A numerical example is given to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

一类不确定性非线性系统的状态反馈鲁棒自适应控制器的设计与分析

该文考虑一类具有一般不确定性和部分参数未知的非线性系统（1），设计出一种用于跟踪参考信号的状态反馈鲁棒自适应控制器，此控制器对系统参数和状态的不确定性具有鲁棒性，能保证闭环系 统的全局稳定性，并解决了ε 跟踪问题. 仿真结果表明，所设计的鲁棒自适应控制系统具有良好的跟踪性能， 而且控制量在容许控制的范围之内.     

Robust reliable H∞ control for neural networks with mixed time delays

This paper considers the problem of robust reliable H_∞ control for neural networks. The system has time-varying delays, parametric uncertainties and faulty actuators. The faulty actuators are considered as a disturbance signal to the system which is augmented with system disturbance input. Based on the LMI technique and the Lyapunov stability theory, a new set of sufficient conditions is obtained for the existence of the robust reliable H_∞ controller. An example is also presented illustrate the results.     

Robust tracking and model following for uncertain time‐delay systems with input nonlinearity

This article proposes a novel adaptive sliding mode control (SMC) scheme to realize the problem of robust tracking and model following for a class of uncertain time‐delay systems with input nonlinearity. It is shown that the proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties and external disturbances. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against input nonlinearity, time‐delays, parameter uncertainties, and external disturbances. Moreover, the knowledge of the upper bound of uncertainties is not required and chattering phenomenon is eliminated. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 66–73, 2015     

Chaos suppression on a class of uncertain nonlinear chaotic systems using an optimal H∞ adaptive PID controller

This paper introduces an optimal H_∞ adaptive PID (OHAPID) control scheme for a class of nonlinear chaotic system in the presence system uncertainties and external disturbances. Based on Lyapunov stability theory, it is shown that the proposed control scheme can guarantee the stability robustness of closed-loop system with H_∞ tracking performance. In the core of proposed controller, to achieve an optimal performance of OHAPID, the Particle Swarm Optimization (PSO) algorithm is utilized. To show the feasibility of proposed OHAPID controller, it is applied on the chaotic gyro system. Simulation results demonstrate that it has highly effective in providing an optimal performance.     

Robust consensus of nonlinear multi‐agent systems via reliable control with probabilistic time delay

In this paper, the consensus problem of uncertain nonlinear multi‐agent systems is investigated via reliable control in the presence of probabilistic time‐varying delay. First, the communication topology among the agents is assumed to be directed and fixed. Second, by introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time‐varying delay is equivalently transformed into the deterministic time‐varying delay with stochastic parameters. Third, by using Laplacian matrix properties, the consensus problem is converted into the conventional stability problem of the closed‐loop system. The main objective of this paper is to design a state feedback reliable controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed‐loop system is robustly stable in the sense of mean‐square. For this purpose, through construction of a suitable Lyapunov–Krasovskii functional containing four integral terms and utilization of Kronecker product properties along with the matrix inequality techniques, a new set of delay‐dependent consensus stabilizability conditions for the closed‐loop system is obtained. Based on these conditions, the desired reliable controller is designed in terms of linear matrix inequalities which can be easily solved by using any of the effective optimization algorithms. Moreover, a numerical example and its simulations are included to demonstrate the feasibility and effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 138–150, 2016     

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.     

Robust finite-time H∞ control of singular stochastic systems via static output feedback

This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H_∞ finite-time boundedness for the class of singular stochastic systems. Designed algorithm for static output feedback controller is provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic H_∞ finite-time boundedness in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology.     

Boundary output feedback stabilization for a class of coupled parabolic systems

In this paper, the boundary output feedback stabilization problem is addressed for a class of coupled nonlinear parabolic systems. An output feedback controller is presented by introducing a Luenberger‐type observer based on the measured outputs. To determine observer gains, a backstepping transform is introduced by choosing a suitable target system with nonlinearity. Furthermore, based on the state observer, a backstepping boundary control scheme is presented. With rigorous analysis, it is proved that the states of nonlinear closed‐loop system including state estimation and estimation error of plant system are locally exponentially stable in the L²norm. Finally, a numerical example is proposed to illustrate the effectiveness of the presented scheme.