Stability Of Discrete-time Switched Systems Based On Switched Time-varying Lyapunov Function

This paper mainly studies the discrete-time switching system.Discrete-time switching system is a hybrid system composed of a series of discrete-time subsystems and switching signals associated with these subsystems.As a relatively simple hybrid system,switching signals play a decisive role in the operation process.In this paper,sufficient conditions for stability of discrete-time switching systems are given by constructing average resident time switching signals,interval resident time switching signals with modal dependence and minimum resident time switching signals with modal dependence.In real life,discrete-time positive switching linear systems are widely involved in rocket launch,satellite orbit change,power system network switching and automobile running state,etc.The phenomenon of time delay is an important factor affecting the stability of the system.However,so far,the research on the theory of time delay for discrete-time positive switching linear systems is not perfect.On the other hand,most of us only need to ensure the stability of finite time in our daily life.There is no need to study the stability of the system under infinite time.There are still many problems to be solved about the finite time stability of the discrete-time switching system.Based on these facts,we begin work on exponential and finite-time stability for discrete-time switching linear systems.This thesis is divided into the following six chapters:The first chapter introduces the basic concepts of switching system,positive system and discrete time switching system,as well as the research background and present situation of the stability of discrete time switching system.The purpose and significance of studying discrete time switching system are also given.The structure of this paper.The second chapter gives the symbol and definition of this thesis.In Chapter 3,the exponential asymptotic stability of discrete-time positive switching linear systems with delays is studied under the mode dependent interval resident time switching signal and the exponential asymptotic stability under the mode dependent minimum resident time switching signal.Then the results are extended to the exponential stability of general discrete time switching time-varying linear systems under the mode dependent interval resident time switching.In addition,the sufficient conditions for exponential stability of switching linear systems under the average resident time switching are given.In Chapter 4,the stability of discrete-time switching linear systems in finite time is studied.By means of the modal dependent interval resident time switching method,the finite-time stability of discrete-time switching positive systems with unstable subsystems is studied.By using the Lyapunov function constructed,the finite-time stability is obtained in the case of delay.The Chapter 5 summarizes the important achievements of the whole paper and looks forward to the future research.In Chapter 1,the basic concepts and research background of switched system,positive system and switched positive system are introduced,and the purpose and significance of studying switched positive system are given.