Stability Of Switched Systems Based On Switched Time-Varying Lyapunov Function

In recent years,switching systems have been widely applied in fields such as robot control,aircraft control,networked control,power electronics systems,automotive industry,biochemical reaction control,etc.The stability of switching systems is the main concern in the field of switching systems.However,there are still insufficient theoretical research on the stability of switching systems,and further improvement is needed.The analysis of system stability mainly utilizes the common Lyapunov function method,but there are significant limitations in practical production and life.As of now,most results need to ensure at least one subsystem is asymptotically stable,and there are still gaps in relevant results when all subsystems are unstable.In conclusion,it is planned to study the stability of continuous time switched linear system when all subsystems are unstable.There are six chapters:In Chapter 1,this chapter introduces the basic concept,research background and research status of switched linear system,and gives the purpose and significance of studying the stability of switched linear system.In Chapter 2,provide the definitions and symbols used in this article.In Chapter 3,in the case that all subsystems are unstable,the switching time-varying Lyapunov function is first designed,and the global asymptotic stability of continuous time switched linear system with norm uncertainty under mode dependent range dwell time switching is studied.Then the global asymptotic stability of continuous time switched linear system with polynomial uncertainty is studied,a sufficient condition is provided for the global asymptotic stability of the system under the switching signal of mode dependent range dwell time.In Chapter 4,under the condition of mode dependent minimum dwell time switching signal and mode dependent range dwell time switching signal,the switching time-varying Lyapunov function is designed,and the practical exponential stability of continuous time switched linear system with disturbance and norm uncertainty with all subsystems are unstable is studied.In Chapter 5,with the help of Lyapunov-Razumikhin theorem,the exponential stability of switched linear system with time delay is studied under the condition that all subsystems are unstable with mode dependent minimum dwell time switching signal and mode dependent range dwell time switching signal.Finally,we give the sufficient conditions for the exponential stability of the system.In Chapter 6,the important results are summarized and the future research is prospected.