A Study Of Dwell-time-based Stabilization And H_? Performance Of Switched Linear Systems

As a particular class of hybrid systems,switched systems are of great significance in both theoretical value and engineering applications.On the other hand,due to the ex-istence of switching signals,the characteristics of switching systems are no longer simple superposition of the characteristics of each subsystem.Different switching strategies make the attributes of the switched linear systems changeable,which are more challenging for the analysis and comprehensive study of the switched linear systems.As a basic require-ment for a system to run normally,stability is one of the important research contents of switched systems.In addition,the H_?analysis of the systems is one of the basic and chal-lenging research topics in the field of hybrid systems control.Up to now,some valuable investigates have been achieved in switched linear systems,but many problems have not been solved.Therefore,this thesis mainly studies the stabilization and H_?performance of switched linear systems under the given switching signals.The main contributions are as follows:In chapter 1,we present a survey.The research significance,methods and existing achievements of switched linear systems,switched positive systems and switched delay systems are summarized respectively.Then,the main works and the structure of this thesis are briefly introduced.In chapter 2,we investigate the stabilization design for a class of switched positive systems based on the given switching signal.Unlike the classical dwell time method,the dwell time is an arbitrarily prespecified constant,which is not computed by Lyapunov functions of the subsystems.First,a state feedback controller is designed by using a class of multiple time-varying linear copositive Lyapunov functions to restrict the decay rate of the subsystem's“energy”,and the sufficient condition of exponential stabilization of the switched positive systems is obtained by constraining the upper and lower bounds of the dwell time.The feasible solution is obtained by using linear programming.Then,the upper bound constraint of dwell time is removed,and a sufficient condition for exponen-tial stabilization of switched positive systems is given.Finally,the effectiveness of the proposed methods is verified by a simulation example.In chapter 3,we study the standard H?performance for a class of switched linear systems with time-varying delay based on the minimum dwell time.First,we types of mul-tiple time-varying Lyapunov functionals are constructed respectively under two switching conditions:delay-dependent minimum dwell time and delay-independent minimum dwell time.Then,we obtain the sufficient conditions by restricting the decay of the Lyapunov functional of the active subsystem and forcing“energy”of the overall switched system to decrease at switching instants by the proposed Lyapunov functionals to guarantee s-tandard L₂-gain performance meanwhile ensuring their internal stability with minimum dwell time switching.Finally,two examples are presented to illustrate the correctness and effectiveness of the proposed results.The conclusions and perspectives end the dissertation.