Stability analysis and control for switched stochastic delayed systems

This paper investigates almost sure exponential stability and feedback stabilization for switched time‐delay systems with nonlinear stochastic perturbations. The main contributions of this paper are threefold: (i) based on the non‐convolution type multiple Lyapunov functionals and the mathematical induction approach, a mean‐square exponential stability condition for nonlinear stochastic switched systems is first established, such that the obtained average dwell time does not rely on any given decay rate; (ii) by using the method developed in part (i) and the stochastic analysis techniques and limit methods in probability, an almost sure exponential stability criterion for switched delayed systems with nonlinear stochastic uncertainties is presented, and then a state feedback controller for the systems under consideration is designed; and (iii) when certain assumptions are made on the nonlinear stochastic perturbations, the results in this paper are further improved by relaxing some conditions. The effectiveness of the proposed method is demonstrated by three illustrative examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Exponential stability of switched stochastic delay systems with non-linear uncertainties

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results.     

Exponentially incremental dissipativity for nonlinear stochastic switched systems

ABSTRACT

In this paper, we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state-dependent switching law and multiple Lyapunov functions approach. Specifically, using incremental supply rate as well as a state dissipation inequality in expectation, a stochastic version of exponentially incremental dissipativity is presented. The sufficient conditions for nonlinear stochastic switched systems to be exponentially incrementally dissipative are given by the designed state-dependent switching law. Furthermore, the extended Kalman–Yakubovich–Popov conditions are derived by using two times continuously differentiable storage functions. Moreover, the incremental stability conditions in probability for nonlinear stochastic switched systems are derived based on exponentially incremental dissipativity. The exponentially incremental dissipativity is preserved for the feedback-interconnected nonlinear stochastic switched systems with the composite state-dependent switching law; meanwhile, the incremental stability in probability is preserved under some certain conditions. A numerical example is given to illustrate the validity of our results.     

Exponential Stability and Asynchronous Stabilization of Switched Systems With Stable and Unstable Subsystems

This paper deals with the exponential stability and asynchronous stabilization of continuous‐time switched systems. By delicately constructed piecewise Lyapunov‐like functions and the minimum dwell time switching method, exponential stability of the switched systems with stable or unstable subsystems is obtained. Based on the result of the stability, the problem of controller design of the switched systems under asynchronous switching is also solved, and the delay that causes asynchronous phenomena can be unbounded. The stability results and control laws of the switched systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrative numerical examples are presented to show the effectiveness of the obtained theoretical results.     

Stability analysis of switched singular stochastic linear systems

ABSTRACT

This paper is devoted to study the stability of switched singular stochastic linear systems with both stable and unstable subsystems. By using the method of multiple Lyapunov functions and the notion of average dwell time, we provide sufficient conditions for the exponential mean-square stability of switched singular stochastic systems in terms of a proper switching rule and the linear matrix inequalities. An example is given to illustrate the effectiveness of the obtained results.     

Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time‐varying delay

This paper is concerned with delay‐dependent exponential stability for stochastic Markovian jump systems with nonlinearity and time‐varying delay. An improved exponential stability criterion for stochastic Markovian jump systems with nonlinearity and time‐varying delay is proposed without ignoring any terms by considering the relationship among the time‐varying delay, its upper bound and their difference, and using both Itô's differential formula and Lyapunov stability theory. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Mean square exponential stability analysis of impulsive stochastic switched systems with mixed delays

In this paper, a class of impulsive stochastic switched systems with mixed delays is considered. On the basis of some integro-differential inequalities and stochastic analysis techniques, some general criteria for mean square exponential stability are obtained. An example is given to illustrate the theory.     

Stability of neutral stochastic switched time delay systems: An average dwell time approach

This paper considers a class of stochastic systems referred to as stochastic switched systems of neutral type with time‐varying delay, which combines switched systems with neutral stochastic systems. The systems consist of subsystems of two forms: (i) only stable subsystems and (ii) both stable subsystems and unstable subsystems. By establishing an integral inequality, the exponential stability in pth(p≥1)‐moment for such systems with only stable subsystems is first considered. Then, by using an average dwell time approach, the exponential stability in pth(p≥1)‐moment for the second form is addressed. An important finding of this study is that when the average dwell time is chosen to be sufficiently large and the total activation time of unstable subsystems is relatively small compared with that of stable subsystems, the exponential stability in pth(p≥1)‐moment for such systems can be guaranteed. Two major advantages of these new results are that the differentiability or continuity of the delay function is not required compared with the existing results in the literature, and the proposed approaches can be used to consider the case when the neutral item and the stochastic perturbation are simultaneously presented. An example is provided to verify the effectiveness and potential of the theoretic results obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

具有脉冲效应的切换随机系统的几乎必然稳定性

针对一类在切换时刻具有脉冲行为的Markov切换非线性随机系统,首先,应用切换的Lyapunov函数方法研究系统的稳定性,给出系统几乎必然稳定的充分条件,该条件不依赖于系统的矩稳定性;然后,进一步对线性系统的稳定化问题进行分析与设计,对随机子系统的控制结构同时出现在方程的位移部分与扩散部分,给出相应的状态反馈增益矩阵的求解方法;最后,数值算例说明了所设计方法的有效性.     

Stability analysis and stabilization control of multi-variable switched stochastic systems

In this paper, the mean square (MS) stability and exponential mean square (EMS) stability of multi-variable switched stochastic systems are investigated. Based on the concept of the average dwell-time and the ratio of the total time running on all unstable subsystems to the total time running on all stable subsystems, some sufficient conditions are given to ensure the MS stability and EMS stability of the switched stochastic systems involved. Further, for the switched stochastic control systems with all subsystems controllable or stabilizable, EMS stabilization controls and sufficient conditions on EMS stabilization are presented, and the convergent rates of the closed-loop systems are obtained.