Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching

This paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching, where the switching instants of the controller experience delays with respect to those of the system. A design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures, and the dwell time approach is utilized for the stability analysis. Then the approach is extended to take into account stochastic switched system with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is employed to verify the proposed method.     

Robust reliable stabilization of uncertain switched neutral systems with delayed switching

This paper investigates the problem of robust reliable control for a class of uncertain switched neutral systems under asynchronous switching, where the switching instants of the controller experience delays with respect to those of the system and the parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee exponential stability and reliability for switched neutral systems, and the dwell time approach is utilized for the stability analysis and controller design. A numerical example is given to illustrate the effectiveness of the proposed method.     

Global stabilization of switched control systems with time delay

In this paper, the stabilization problem of switched control systems with time delay is investigated for both linear and nonlinear cases. First, a new global stabilizability concept with respect to state feedback and switching law is given. Then, based on multiple Lyapunov functions and delay inequalities, the state feedback controller and the switching law are devised to make sure that the resulting closed-loop switched control systems with time delay are globally asymptotically stable and exponentially stable.     

Modeling and SPM-dependent control of multi-rate networked control system with long time delay

In this paper, an efficient approach of modeling and control is presented for Multi-Rate Networked Control System (MRNCS) with considering long time delay. Firstly, the system is modeled as a switched system with a random switching signal which is subject to random networked-induced delay. For this, time delay is defined as a Markov chain and the model of MRNCS is obtained as a Markovian jump linear system. Afterward, a dynamic output feedback controller is designed for output tracking as well as stabilization of closed-loop system. The modeling and control of MRNCS are presented for two structures. At first, a new model of single-side MRNCS is proposed and a mode-independent controller is designed for stabilizing the system. Then the proposed modeling method is generalized to double-side MRNCS and by introducing the Set of Possible Modes (SPM) concept, an SPM-dependent controller is proposed for double-side MRNCS. To show the effectiveness of the proposed methods, some numerical results are provided on the quadruple-tank process.     

Robust exponential stability of switched delay interconnected systems under arbitrary switching

The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and unbounded delay is addressed. On the assumption that the interconnected functions of the studied systems satisfy the Lipschitz condition, by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems under arbitrary switching are obtained. The proposed method, which neither require the individual subsystems to share a Common Lyapunov Function (CLF), nor need to involve the values of individual Lyapunov functions at each switching time, provide a new way of thinking to study the stability of arbitrary switching. In addition, the proposed criteria are explicit, and it is convenient for practical applications. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed theories.     

Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems

We investigate the tracking control problem for switched linear time-varying delays systems with stabilizable and unstabilizable subsystems. Sufficient conditions for the solvability of the tracking control problem are developed. The tracking control problem of a switched time-varying delays system with stabilizable and unstabilizable subsystems is solvable if the stabilizable and unstabilizable subsystems satisfy certain conditions and admissible switching law among them. Average dwell time approach and piecewise Lyapunov functional methods are utilized to the stability analysis and controller design. By introducing the integral controllers and free weighting matrix scheme, some restricted assumptions imposing on the switched systems are avoided. A simulation example shows the effectiveness of the proposed method.     

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.     

Stability of switched systems with time delay

In this paper, we study the qualitative properties of linear and nonlinear delay switched systems which have stable and unstable subsystems. First, we prove some inequalities which lead to the switching laws that guarantee: (a) the global exponential stability to linear switched delay systems with stable and unstable subsystems; (b) the local exponential stability of nonlinear switched delay systems with stable and unstable subsystems. In addition, these switching laws indicate that if the total activation time ratio among the stable subsystems, unstable subsystems and time delay is larger than a certain number, the switched systems are exponentially stable for any switching signals under these laws. Some examples are given to illustrate the main results.     

Finite‐time stability and boundedness of switched nonlinear time‐delay systems under state‐dependent switching

This article investigates the finite‐time stability, stabilization, and boundedness problems for switched nonlinear systems with time‐delay. Unlike the existing average dwell‐time technique based on time‐dependent switching strategy, largest region function strategy, that is, state‐dependent switching control strategy is adopted to design the switching signal, which does not require the switching instants to be given in advance. Some sufficient conditions which guarantee finite‐time stable, stabilization, and boundedness of switched nonlinear systems with time‐delay are presented in terms of linear matrix inequalities. Detail proofs are given using multiple Lyapunov‐like functions. A numerical example is given to illustrate the effectiveness of the proposed methods. © 2014 Wiley Periodicals, Inc. Complexity 21: 267–275, 2015     

Sampled-data control of uncertain switched neutral nonlinear systems under asynchronous switching

The robust exponential stabilization for a class of the uncertain switched neutral nonlinear systems with time-varying delays based on the sampled-data control is investigated in this paper. The closed-loop system with sampled-data control is modeled as a continuous time system with a time-varying piecewise continuous control input delay. Considering the relationship between the sampling period and the dwell time of two switching instants, sampling interval with no switching and sampling interval with one switching are discussed, respectively. By Wirtinger-based inequality, Wirtinger-based double integral inequality, and free-weighting matrix technique, some delay-dependent sufficient conditions are given to guarantee the exponential stability of uncertain switched neutral nonlinear systems under asynchronous switching. In addition, sampled-data controllers can also be designed by special operations of matrices. Finally, two numerical examples are used to show the effectiveness of the approach proposed in this paper.     

Robust stabilization for uncertain switched impulsive control systems with state delay: An LMI approach

This paper deals with the problem of robust H_∞ state feedback stabilization for uncertain switched linear systems with state delay. The system under consideration involves time delay in the state, parameter uncertainties and nonlinear uncertainties. The parameter uncertainties are norm-bounded time-varying uncertainties which enter all the state matrices. The nonlinear uncertainties meet with the linear growth condition. In addition, the impulsive behavior is introduced into the given switched system, which results a novel class of hybrid and switched systems called switched impulsive control systems. Using the switched Lyapunov function approach, some sufficient conditions are developed to ensure the globally robust asymptotic stability and robust H_∞ disturbance attenuation performance in terms of certain linear matrix inequalities (LMIs). Not only the robustly stabilizing state feedback H_∞ controller and impulsive controller, but also the stabilizing switching law can be constructed by using the corresponding feasible solution to the LMIs. Finally, the effectiveness of the algorithms is illustrated with an example.     

网络化非周期采样控制系统的主动时间滞后控制:随机脉冲切换系统方法

研究了一类带有随机丢包的非周期采样网络化控制系统的镇定问题.不同于传统观点往往将时滞看作系统稳定性的消极因素,考虑时间滞后对系统稳定性的积极影响,并提出一个新颖的主动时间滞后控制方法来镇定该系统.为了分析时间滞后控制的积极作用并获得较低保守性的结论,首先把带随机丢包的非周期采样系统建模为带固定切换率的随机脉冲切换系统,...     

多时滞线性切换系统的稳定性及其反馈镇定

研究了具有多时滞线性切换系统的稳定性及其反馈镇定问题,利用完备性条件、矩阵分解与二次Lyapunov泛函,给出了多时滞切换系统渐近稳定的充分条件和切换律设计方法.在此基础上,研究了这类系统的镇定控制问题,设计了保证系统时滞独立渐近镇定的控制器.     

Adaptive projective synchronization for a class of switched chaotic systems

This paper addresses the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods. First, a necessary and sufficient condition is proposed to show how many state variables can realize projective synchronization under a linear feedback controller for the chaotic systems. Then, accordingly, a new algorithm is given to select all state variables that can realize projective synchronization. Furthermore, according to the results of the projective synchronization of chaotic systems, the problem of projective synchronization of the switched chaotic systems comprised by the unified chaotic systems is investigated, and an adaptive global linear feedback controller with only one input channel is designed, which can realize the projective synchronization under the arbitrary switching law. It is worth mentioning that the proposed method can also realize complete synchronization of the switched chaotic systems. Finally, the numerical simulation results verify the correctness and effectiveness of the proposed method.     

Global exponential stability of certain switched systems with time-varying delays

This paper is focused on global exponential stability of certain switched systems with time-varying delays. By using an average dwell time (ADT) approach that is different from the method in [P.H.A. Ngoc, On exponential stability of nonlinear differential systems with time-varying delay, Applied Mathematics Letters 25 (2012) 1208–1213], we establish a new global exponential stability criterion for the switched linear time-delay system under the ADT switching. We also apply this method to a general switched nonlinear time-delay system. A numerical example is given to show the effectiveness of our results.     

Adaptive event-triggered dynamic distributed control of switched positive systems with switching faults

This paper designs the dynamic output-feedback controller of switched positive systems subject to switching faults using an improved adaptive event-triggering mechanism. An adaptive event-triggering condition is addressed in the form of 1-norm by virtue of the measurable outputs of distributed sensors and the corresponding error. An error-based closed-loop control system whose dynamic variable relies on a state observer is obtained. A multiple copositive Lyapunov function is constructed to deal with the positivity and stability of the systems. The matrix decomposition and linear programming approaches are used to design and compute the controller and observer gains. An improved average dwell time scheme is proposed to handle the switching faults. The contributions of this paper lie in that: (i) An adaptive event-triggering mechanism is established for switched positive systems, (ii) A framework on the fault of switching signal is constructed, and (iii) A dynamic distributed controller is proposed for the considered systems. Finally, two illustrative examples are given to verify the effectiveness of the obtained results.     

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.     

Robust observer design for nonlinear uncertain switched systems under asynchronous switching

Switching between the system and the associated observer or controller is in fact asynchronous in switched control systems. However, many times we assume it synchronous, for simplicity. In this paper, the robust observer design problems for a class of nonlinear uncertain switched systems for synchronous and asynchronous switching are addressed. At first, a robust observer under synchronous switching is proposed based on average dwell time approach. After that, the results are extended to robust observer design in the asynchronous case. In this case, two working modes are adopted to facilitate the studies on the issue. Finally, an extension case covering more practical applications is investigated under asynchronous switching. The designed observer cannot maintain the asymptotical stability of error state, but the eventual boundness is guaranteed. At the end, a numerical design example is given to illustrate our results.     

Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.