Stability Analysis Of A Class Of Stochastic Switched Systems

Stochastic switched systems are considered to be a class of hybrid systems,which consist of a family of distinct active subsystems under operation governed by a stochastic process.According to a stochastic switching rule,a subsystem will be activated at a certain instant.The stability of system and stabilization control is one of the important research directions of the stochastic switched system,these research results are widely used in many fields,such as network communication,transportation and circuit system.In this paper,we concern with the pth moment stability,exponential stability,input-to-state stability and integral input-to-state stability of switched systems under the stochastic switching rule with Markovian property.Firstly,the input-to-state stability is studied for nonlinear stochastic system under Markovian switching rule.Secondly,we consider about the input-to-state stability and the integral input-to-state stability of stochastic time-delay system under Markovian switching rule.Finally,we analyze the properties of Semi-Markovian chain,and the stability of a class of linear stochastic differential system driven by Semi-Markovian process is proved.The main contents of this paper are summarized as follows:Chapter 1 illustrates the motivations on the research of stochastic switched systems,stochastic systems under Markovian switching rule and stochastic systems under Semi-Markovian switching rule.In addition,it presents the literature review of the two types of stochastic switched systems.At last,we sort out the framework and content of this paper.Chapter 2 studies the input-to-state stability of nonlinear stochastic switched system under Markovian switching rule with external inputs.With the help of the definition of ergodicity property of Markovian chain and Lyapunov function method,we discussed the boundedness of switched system state under the influence of external inputs.The input-to-state stability of nonlinear stochastic differential system under Markovian switching rule is obtained.Chapter 3 assumes that the stability of the switched systems is time-varying.By using the comparison theorem and the Lyapunov-Krasovskii function method,we study the input-to-state stability and the integral input-to-state stability of stochastic switched system with time-delay under Markovian switching rules.Chapter 4 makes use of the irreducibility of Semi-Markovian chain and the coupling characteristics of Markovian chain to get the stationary distribution of embedded chain,and deduce the stationary distribution of Semi-Markovian chain.The almost surely exponential stability of linear stochastic system is proved by the stationary distribution of Semi-Markovian chain and the strong law of numbers.At the same time,we study the pth moment stability of linear stochastic system.Chapter 5 summarizes the research results of the full text,and pointed out the inadequacies of this paper.The future research planning and prospect are put forward.