Robust Exponential Stability For Switched Systems With Interval Time-varying Delay

A switched system is a hybrid dynamical system consisting of a family ofcontinous-time subsystems or discrete-time subsystems and a rule that governs theswitching between them. The source of motivation for studing switched systems comesfrom the rapidly developing area of intelligent control. The methods of intelligentcontrol design are based on the idea of switching between different controllers. Thesecontrol techniques haves been applied extensively in recent years, particularly in theadaptive context. Switched systems have been applied in electrical power systems, robotcontrol systems, control of networks. The last decade has witnessed increasing researchactivities in study of controllability, observability, stability, stabilisation and filteringdesign of switched systems.This paper deals with a switched systems with interval time-varing delay. Taking onthe average dwell time method, and using Lyapunov function method, we study therobust exponential stability of switched systems with time-varing delay and theexponential stbility and the hybrid controllers’ design problems of swiched systems withmultiple time-varing delays, and the robust exponential stability of switched systemswith mixed time-varying delays.The first chapter is a brief introduction for the importance and the practical andtheoretical significance and the current scholar results of the stability of the switchedsystems with time-varing delay. In the second chapter, Stability criteria and hybridcontrollers’ design problems for a class of switched systems with interval time-varingdelay are considered. Based on taking the piecewise Lyapunov-Krasovskii functional,we investigate the exponential stability by the method of average dwell time. In thethird chapter, the stability analysis for multiple interval time varying-delay of switchedsystems is investigated. By using the Lyapunov function method and the integralinequality and reciprocally convex approach, a new stability criteria is given in the formof linear matrix inequalities (LMIs). In the forth chapter, By using a newLyapunov-Krasovskii function, the robust exponential stability of switched systemswith mixed time-varying delays are introduced, and we obtain a much less conservative result.Finally, the numerical examples are given in every chapter to demonstrate theapplicability and the effectiveness of the proposes method.