Stability Research Of A Class Of Non-linear Switched Stochastic Systems

A switched stochastic system is a dynamical system that consists of a finite number of subsystems and a logical rule that orchestrates switching between these subsystems.The research of system stability has always been one of the important directions of switching stochastic systems.Its related research results have been widely used in transportation,automotive automatic transmission systems,electrical power system,network communications and many other fields.The stability of the entire system is not only related to the stability of each subsystem,but also related to the switching rules between each subsystem.The research results of linear switching stochastic systems with deterministic switching signals have been quite rich.However,there are not all linear switching stochastic systems in life.There are also many nonlinear switching stochastic systems,which results in switching random systems that do not meet linear growth conditions and global Lipschitz conditions.The nonlinear switched stochastic system makes the system more widely used in real life,so it is very meaningful to study the stability of the nonlinear switched stochastic system.In this paper,for a class of nonlinear switched stochastic systems with non-random switching signals,the existence and uniqueness of the system solutions and the pth moment exponential stability are studied.First,the stability of highly nonlinear switched stochastic systems with non-random switching signals is studied.Then,the stability of highly nonlinear switched stochastic time-delay systems with non-random switching signals is studied.The main contents of this article are summarized as follows:In Chapter 1,the research background and significance of switched systems,switched stochastic systems,and nonlinear switched stochastic systems are first described.Then it introduces the domestic and foreign research status of the stability of switched systems,switched random systems and nonlinear hybrid systems.Finally,the main contents and basic framework of the research in this paper are summarized.In Chapter 2,the stability of highly nonlinear switched stochastic systems under non-random switching signals is studied.Without the guarantee of linear growth conditions and global Lipschitz conditions,the Lyapunov function method is used to obtain that each subsystem exists unique solution.And the unique solution will not explode in the finite time.By the average dwell time approach,mathematical induction method and stochastic analysis method,the solution of highly nonlinear switched stochastic systems with non-random switching signals will not explode in the finite time,and the pth moment exponential stability of highly nonlinear switched stochastic systems with non-random switching signals is obtained.In Chapter 3,for highly nonlinear switched stochastic time-delay systems with non-random switching signals,there is still no guarantee of linear growth condition and global Lipschitz condition.By constructing Lyapunov function method,two different structures of Lyapunov functions are obtained.The existence and uniqueness of solutions and the p-moment exponential stability of highly nonlinear switched stochastic time-delay systems with non-random switching signals are obtained,separately.In Chapter 4,the research results of this paper is summarized.At the same time,in view of the shortcomings in this study,the future research plan and prospects are proposed.