Finite Time Stability And L₂-gain Analysis Of Uncertain Switched Linear Systems Under State-dependent Switching

In recent years,most scholars tend to focus on the analysis of stability andstabilization of switched linear systems.Due to practical applications, we’d like tostudy the behaviors and performances of switched systems in a finiteintervals.Therefore it is of great importance to consider this problem.This paperstudies the problem of finite time stability and boundedness(FTSB),and alsoL2-gainanalysis of uncertain switched linear systems under state-dependent switching,usingthe method of covex combinations and state-dependent strategy..Some sufficientconditions have been given for FTSB of switched linear systems based on the methodof multiple Lyapunov-like functions,and it also suits for sliding motion behaviors.The main results of this paper are ranged as follows.（1）In the first chapter,it mentions the background of switched systems and givesa summerise of the problems that we’d like to study of switched systems.And then wefocus on the problems of FTSB due to the practical applications.At last the majorwork and arrangement have been listed.Give conditions of problem formulation andsome explanations have been given,too. We also provide the assumptions and somelemmas,also the major definations of this paper.（2）In the second chapter,we study the problem of FTSB of uncertain switchedsystems.Problem formulation and some explanations have been given,too. Somesufficient conditions for FTSB have been mentioned.And we consider the problem ofsliding motions.（3）In the third chapter, study the problem of finite time study the problem offinite timeL2-gain analysis,give sufficient conditions and consider the slidingmotions as well.（4）In the last chapter,we summarize the main work and results of this paper, thenmentions the future developments based on the current achivements.