Exponential Stability And L₂ Gain For Switched Systems With Time-varying Delay

As an important class of hybrid dynamical systems,switched system is composed of a series of subsystems and a rule that governs the switching among them.The time delays and uncertainties are prevalent in practical engineering systems,which usually disturb stability for switched systems and lead to performance reduction.Even so,the systems with time-varying delay and uncertainties can describe practical engineering systems well and truly.Such as power systems and networked systems and chemical engineering systems.Such systems can be modelled as switched delay systems.Because of the systems with time-varying delay have great theoretical and practical value in the actual,whith have received much attention.This article studies three problems of the exponential stability for switched systems with time-varying delays,including exponential stability stability andL₂ gain analysis for switched systems with time-varying delay;Exponential stability stability andL₂ gain analysis for switched systems with multiple time-varying delays;Robust exponential stability for switched systems with time-varying delay.By choosing an appropriate Lyapunov-Krasovskii function with double integral or triple integral and using the average dwell time method and LKFS theory the sufficient conditions of exponential stability for switched systems with time-varying delays in arbitrary switching law are gained in the form of linear matrix inequality.By using delay decomposition approach and the method of Jensen integral inequality and combining reciprocally convex develops less conservative stability criterion.In the first chapter we introduce the concept and research background and research value of the time-varying delays switched systems.At the same time,system model and the main content of this article are presented.The innovative thinking of the second chapter is delay decomposition approach and the method of combining Jensen integral inequality and reciprocally convex are used to deal with the integer terms in the Lyapunov function.A new criterion of exponential stability for switched systems with time-varying delays are gained.We combine Jensen integral inequality and double reciprocally convex together in the third chapter which is uesd to solve the trebling integer terms in the complex Lyapunov-Krasovskii function.Thus the problem of exponential stability andL₂ gain analysis for switched systems with multiple time-varying delays is studied.Based on the method in the third chapter,in thefourth chapter we study robust exponential stability for switched systems with time-varying delays.By used the average dwell time method exponential decay rate and theoretic criterion of robust exponential stability are gained.