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.     

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     

Robust sampled‐data H∞ control for mechanical systems

This article addresses the issue of robust sampled‐data control for a class of uncertain mechanical systems with input delays and linear fractional uncertainties which appear in all the mass, damping, and stiffness matrices. Then, a novel Lyapunov–Krasovskii functional is constructed to obtain sufficient conditions under which the uncertain mechanical system is robustly, asymptotically stable with disturbance attenuation level about its equilibrium point for all admissible uncertainties. More precisely, Schur complement and Jenson's integral inequality are utilized to substantially simplify the derivation of the main results. In particular, a set of sampled‐data controller is designed in terms of the solution of certain linear matrix inequalities that can be solved effectively using available MATLAB software. Finally, a numerical example with simulation result is provided to show the effectiveness and less conservativeness of the proposed sampled‐data control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 19–29, 2015     

H∞ stochastic synchronization for master–slave semi‐Markovian switching system via sliding mode control

In this article, synchronization problem of master–slave system with phase‐type semi‐Markovian switching is investigated via sliding mode control scheme. By utilizing a supplementary variable technique and a plant transformation, the master–slave semi‐Markovian switching system can be equivalently expressed as its associated Markovian switching system. Then an integral sliding surface is constructed to guarantee stochastic synchronization of master–slave semi‐Markovian switching system, and the suitable controller is synthesized to ensure that the trajectory of the closed‐loop error system can be driven onto the prescribed sliding mode surface. Finally, numerical simulations are presented to show the effectiveness of the proposed sliding‐mode design scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 430–441, 2016     

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

This article presents an adaptive sliding mode control (SMC) scheme for the stabilization problem of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity. The algorithm is based on SMC, adaptive control, and linear matrix inequality technique. Using Lyapunov stability theorem, the proposed control scheme guarantees the stability of overall closed‐loop uncertain time‐delay chaotic system with input dead‐zone nonlinearity. It is shown that the state trajectories converge to zero asymptotically in the presence of input dead‐zone nonlinearity, time‐delays, nonlinear real‐valued functions, parameter uncertainties, and external disturbances simultaneously. The selection of sliding surface and the design of control law are two important issues, which have been addressed. Moreover, the knowledge of upper bound of uncertainties is not required. The reaching phase and chattering phenomenon are eliminated. Simulation results demonstrate the effectiveness and robustness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 13–20, 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     

Nonfragile H∞ filtering for wireless‐networked systems with energy constraint

This article is concerned with the nonfragile filtering for wireless‐networked systems with energy constraint. To achieve the energy‐efficient goal, the local measurement is first sampled by nonuniform sampling, then we only choose one measurement to transmit it to the remote filter. In the filter design, the random occurring filter gain variation problem is taken into account. A new stochastic switched system model is presented to capture the nonuniform sampling, the measurement size reduction, and the random filter gain phenomena. Based on the switched system approach, stochastic system analysis, and Lyapunov stability theory, a sufficient condition is presented such that the filtering error system is exponentially stable in the mean‐square sense and a prescribed performance level is also guaranteed. The effectiveness of the proposed new method is illustrated by a simulation example. © 2015 Wiley Periodicals, Inc. Complexity 21: 79–89, 2016     

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 reliable sampled‐data H∞ control for uncertain stochastic systems with random delay

In this article, the problem of robust reliable sampled‐data control for a class of uncertain nonlinear stochastic system with random delay control input against actuator failures has been studied. In the considered system, the parameter uncertainty satisfies the norm bounded condition and the involved time delay in control input are assumed to be randomly time‐varying which is modeled by introducing Bernoulli distributed sequences. By constructing a novel Lyapunov–Krasovskii functional involving with the lower and upper bounds of the delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for ensuring the robust asymptotic stability of the uncertain nonlinear stochastic system with random delay and disturbance attenuation level about its equilibrium point for all possible actuator failures. In particular, Schur complement together with Jenson's integral inequality is utilized to substantially simplify the derivation in the main results. The derived analytic results are applied to design robust reliable sampled‐data controller for hanging crane structure model and simulation results are provided to demonstrate the effectiveness of the proposed control law. © 2014 Wiley Periodicals, Inc. Complexity 21: 42–58, 2015     

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.     

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.     

线性滞后广义系统的二阶滑模控制方法

讨论了时滞广义系统在不同条件下的变结构控制,根据终端滑模控制的特点,提出了一种由线性滑模与终端滑模构成的二阶终端滑模及相应控制策略.研究结果表明,该方法能够有效地清除系统的高频抖振,同时保证闭环系统的渐近稳定,实现滑模运动.举例说明了设计的合理性和有效性.     

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     

Robust ℋ∞ tracking control for uncertain Markovian jumping systems with interval time‐varying delay

In this article, the problem of robust tracking control for a class of uncertain Markovian jump systems with interval time‐varying delay is investigated. Based on an augmented Lyapunov–Krasovskii functional with triple integral term, partitioning the delay's lower bound and reciprocally convex approach, delay‐dependent conditions for the existence of desired controller are achieved. Meanwhile, stability criteria for delayed Markovian jump systems are also provided with less conservativeness and less matrix variables than some recent results. Finally, two simulation examples are given to illustrate the effectiveness of the proposed design method. © 2014 Wiley Periodicals, Inc. Complexity 21: 355–366, 2015     

Terminal sliding mode control without singular for a class of uncertain system

An improved nonsingular terminal sliding mode method is proposed for a class of nonlinear systems with unmodeled dynamics. The proposed method can effectively avoid the singularity problem. The stability of the proposed procedure which could guarantee the robustness against uncertain unmodeled dynamic and external disturbances is proven by using the Lyapunov theory in finite time. An example is given to show the proposed improved terminal sliding mode control law without singular effectively. © 2016 Wiley Periodicals, Inc. Complexity 21: 566–572, 2016     

Triple integral approach to reachable set bounding for linear singular systems with time‐varying delay

This paper is concerned with the reachable set estimation problem of singular systems with time‐varying delay and bounded disturbance inputs. Based on a novel Lyapunov–Krasovskii functional that contains four triple integral terms, reciprocally convex approach and free‐weighting matrix method, two sufficient conditions are derived in terms of linear matrix inequalities to guarantee that the reachable set of singular systems with time‐varying delay is bounded by the intersection of ellipsoid. Finally, two numerical examples are given to demonstrate the effectiveness and superiority of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Design of observers for nonlinear systems with H ∞ performance analysis

This paper investigates the problem of observer design for nonlinear systems. By using differential mean value theorem, which allows transforming a nonlinear error dynamics into a linear parameter varying system, and based on Lyapunov stability theory, an approach of observer design for a class of nonlinear systems with time‐delay is proposed. The sufficient conditions, which guarantee the estimation error to asymptotically converge to zero, are given. Furthermore, an adaptive observer design for a class of nonlinear system with unknown parameter is considered. A method of H _∞ adaptive observer design is presented for this class of nonlinear systems; the sufficient conditions that guarantee the convergence of estimation error and the computing method for observer gain matrix are given. Finally, an example is given to show the effectiveness of our proposed approaches. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Event-triggered sliding mode control for singular systems with disturbance

This paper investigates the event-triggered sliding mode control (SMC) problem for singular systems with disturbance. Firstly, an event-triggered sliding mode control law is designed to guarantee the reachability of sliding surface. Different from the related methods, in order to deal with the difficulty caused by event-triggered SMC strategy, a novel Lemma is proposed in this paper. Secondly, the admissibility of sliding motion is presented, which is used to solve the controller gain. Then, a positive lower bound of the inter execution time can be guaranteed and the Zeno behavior is avoided. Finally, two simulation examples are presented to show the effectiveness of derived theoretical results.