Quasi-time Dependent H_? Control Of Average Dwell Time Switched Linear System

With the development of society,control theory encounters a variety of challenges.The satisfactory control effect can not be obtained if the method which simply relies on continuous-time or discrete-time system.Therefore,hybrid systems has absorbed much attention.Switched system as a class of special hybrid system includes continuous-time sub-systems or discrete-time sub-systems and the switching laws working on it.The presence of switching make that the system dynamic behavior becomes more difficult,which let the control and analysis of system be more challenge.Meanwhile,research results of switched systems also make significant reference to generate hybrid systems in terms of ideas,methods and theories.On the other hand,uncertainties and timedelays are frequently encountered in many practical engineering systems,which makes the system more complex.Mechanism of system evolution is far from clear and many fundamental problems are still either unexplored or less well understood.Therefore,the study of switched systems deserves investigation for theoretical development as well as for practical applications.This dissertation surveys the recent results on hybrid system and gives a in-depth study on the H_?control problem of discrete average dwell time linear switched system.The main content and results are as follows:The main results in the frontier of discrete time linear switched systems are summarized and analyzed,and point out that the research on the control of discrete-time switched linear systems is still in its infancy.Stability analysis is the basis of the dynamics system research,its importance is self-evident.For the switching system,the switching rules are varied,and under certain conservatism,there is no uniform switching rule that can make the switching system stable,which makes the stability analysis very complicated.This paper first reviews the theory of switching systems,including stability analysis and stabilization problems.By combining the average dwell time and the technique of multiLyapunov function,this paper studies the stability of the switching system based on the quasi-time-dependent analysis method,which has laid a good foundation for the whole work.Then,this paper analyse the l₂ gain performance of switched linear system.In the H_?control of the linear system,the H_?performance reflects the ability of the system to suppress outside interference and plays a key role in the analysis of the system.In time domain,H_?norm equals to l₂ gain.Considering the problem that needs to be studied in this paper,we recall how to analyse l₂ gain performance of linear switched system based on mode-dependent average dwell time firstly.Then,this paper propose the stability conditions of the switching system to ensure a certain L₂ gain performance in the sense of the time-dependent average dwell time.Next,we research how to design a H_?controller of linear switched system.First we reviewed robust analysis and design methods and standard H_?control problems.Robust control problems can be transformed into H_?control problem.Based on the method of state feedback,this paper designs a quasi-time dependent H_?controller for modal dependent average residence time switching linear systems.Finally,The feasibility and validity of the proposed control algorithm are verified by numerical simulation.In this paper,a practical example and an actual circuit model are used to verify the validity and feasibility of the proposed control algorithm.A detailed comparison with the existing results is given from the aspects of conservativeness and performance.The validity of the proposed method is verified,the conservativeness of the controller is reduced,and the basic work is made for further research in the future.