Analysis And Control For A Class Of Switched Systems With Dwell Time

Switched system is a special class of hybrid systems,it is composed by a finite number of subsystems and a rule orchestrating the switch among them.There are several different switching laws:time-dependent switching law,state-dependent switching law,state-and time-dependent switching law and so on.Besides,there are three basic problems in the stability analysis and control design of switched systems:(i)find conditions for stability under arbi-trary switching;(ii)identify the limited but useful class of stabilizing switching laws;and(iii)construct a stabilizing switching law.There have been many works on problem(ii),and the switching law with dwell time method is considered mostly.Considering the wide application of the switched systems with dwell time in practice,the study on switched systems with dwell time has an important scientific significance and application value.In this paper,based on the previous work on switched systems,by utilizing linear ma-trix inequalities(LMIs)technique,for switched linear systems,switched singular systems and switched nonlinear systems,the stability analysis and H? control problem are solved,respec-tively.The main contributions of this thesis are summarized as follows:(1)The stability analysis and H? control problem for switched linear systems with dwell time are studied.Based on the average dwell time(ADT)technique which is the most famous method and the discretized Lyapunov function(DLF)technique which is the more popular re-cently method,the stability analysis and the sufficient conditions for existence of the H? con-troller are proposed,respectively.On the one hand,using the ADT method,only a weighted H?performance is guaranteed;on the other hand,using the DLF method,although the computation complexity increases,a norm H? performance is guaranteed.(2)The stability analysis and H? control problem for switched linear systems with dwell time are investigated.For a class of switched singular systems with uncertainties in the deriva-tive matrices,based on the conventional ADT method and considering the jump of the state at the switching instants,an improved average dwell time is proposed.Using this method,a two-step optimization problem is proposed to obtain the desired controller such that the performance is guaranteed and the dwell time constraint is as small as possible.(3)The stability analysis and H? control problem for switched linear systems with dwell time are considered.For a class of switched nonlinear systems,the T-S fuzzy models are con-structed to describe these systems and the T-S fuzzy theories are applied to the study.The switched fuzzy systems have unstable subsystems and mode-dependent average dwell time.For these systems,based on the MDADT technique,an improved discretized Lyapunov func-tion technique,where the time-varying intervals of the Lyapunov matrices are mode-dependent,is proposed.With this method,a more general stability analysis and more general sufficient conditions for existence of the desired H? controller are given.Finally,the main work of the thesis is summarized,and the future work and reserch topics are provided.