Stability Analysis For Discrete-time Switched Systems

A switched system consists of a finite number of subsystems and a switching rule,the rule determines which subsystem is activated.The switching signal with some restrictions can be regarded as a powerful tool to stabilize the switched systems.As an important class of hybrid system,the research of switched systems has become the hotspot,which,along with the development of data control theory and electronic technology,discrete-time systems are becoming more and more important and having more extensive application.This paper mainly study the special family of switched systems,namely switched system on the discrete-time stability analysis and finite time bounded analysis,via constructing a Lyapunov function or Lyapunov-like function to get a series of sufficient conditions of the stability of the system.In the first chapter,we mainly introduces the definition of switched system,research field and development prospects of the existing three basic problems,and introduces the average dwell time(ADT)and mode-dependent average dwell time(MDADT)of the two switching strategy.In the second chapter,based on the ADT method,a class of linear discrete-time switched systems is analysed,and a state feedback controller is designed.In the third chapter,we discusses the stability and gain problem of switched linear systems with discrete time,by constructing multiple Lyapunov functions,sufficient conditions for the stability of systems and gain property,the condition is typical linear matrix inequalities,LMIs can be used directly to solve the problem.The MDADT method is introduced,which gains the system globally exponentially stable conditions with less conservative.In the fourth chapter,we studies the bounded time stability analysis and robust control conditions of uncertain discrete-time switched systems,this kind of discrete-time systems equip external disturbances and control input,the external disturbance is time-varying and meet certain conditions.By using Schur lemma,we design the state feedback controller to obtain sufficient conditions for finite time stability of the system.