Stability Study For Switched Stochastic Systems With Average Dwell Time

An important part of hybrid dynamical systems is switching system,which consists of subsystems and switching rules.The switching system is used to determine the current operating subsystem according to certain switching rules.In recent years,switched systems have been widely used in many fields,such as large power supply network,robot industry,transportation,complex chemical process and so on.For switched systems,it is a key problem in the research of switched systems to find effective switching rules,and to keep the switching system stable under certain switching rules.Based on the average dwell time,the paper considers the influence of the own characteristics of different subsystems of switched systems on the stability of switched systems.Under mode-dependent assumptions,the p th moment stability and input-to-state stable of switched stochastic systems are studied.At the same time,we will also consider the influence of these unstable subsystems on the stability of switched stochastic systems when the switched system has partial unstable subsystems.The main contents of this paper are summarized as follows:The first chapter is the introduction,including three parts:describing the research background and significance;the related research results are briefly introduced;the content and structure of the full thesis are combed.In the second chapter,by using the concept of the mode-dependent average dwell time,the input-to-state stability of switched stochastic systems is studied when all subsystems of switched stochastic systems are stable,and the state estimation of switched stochastic systems is given,and the sufficient conditions of the input-to-state stability are obtained on the basis of state estimation.In the third chapter,when the switched system has partial stable subsystems,Under mode-dependent assumptions,the time-varying upper bound of the operator for the Lyapunov function,the operating time of the subsystems and the average dwell time are all mode-dependent.The state estimation of switched stochastic systems is derived by applying some auxiliary equations and the Lyapunov-Razumikhin method.By using the method of the mode-dependent average dwell time,the p th moment stability,the p th moment asymptotic stability and the p th moment exponential stability are researched for the switching stochastic delayed systems.In addition,for the switching stochastic delayed systems of the partial stable subsystems,the sufficient conditions of the input-to-state stability and the integral-input-to-state stability are given under the given state estimation of systems by using the method of the mode-dependent average dwell time and the time-varying upper bound of the operator for the Lyapunov function about mode-dependence.The last chapter summarizes the results and gives the inadequacies of full thesis,further looks forward to the future research plan.