Stability Analysis And The Design Of Reliable Controller Of Switched Systems

A switched system is a special hybrid dynamical system. It is consisted of afamily of continuous-time or discrete-time subsystems and a rule which governs theswitching between them. Generally speaking, most of single system can not satisfythat performance which we expect. However we can achieve our objectives bycreating a switched system. Because of that, switched systems have much morepractical meaning. In engineering systems, there is inevitably affect because ofexternal environment and internal environment. In order to more accurately describethese situations, the description of the system itself and the process operation of thesystems are more and more complex. So, some new switched systems have founded.Therefore, more and more researchers have been interested in studying the problemsof the stability of the switched systems. With the development of modern industrialand engineering technology, more and more attentions have been paid to the problemsof analysis and synthesis for switched systems.This paper studies the analysis and synthesis of switched systems. Base on thetheory of linear matrix inequality, we shall study the problem of stability for linearswitched systems with time-varying delay and switched systems with two additivetime-varying delays by Lyapunov method, and we will obtain a new way of designingreliable controller for linear switched systems.The first section of the paper is a brief introduction on the purposes of studying,the practical and theoretical significance and several current theoretical results of theswitched systems. In the second section, some basic control concepts of stability andbasic control systems theory should be introduced. In the third section, the result onanalysis of stability for linear switched systems with two additive time-varyingdelays is studied. By Lyapunov second method, we obtained a new sufficientcondition on stability of this switched systems. In the forth chapter, the problem of thestability for linear switched systems with time-varying delay e studied. Based on thetechnology of free weight matrix, we obtained a new result about stability of switchedsystems and less conservative results can be obtained. In the fifth chapter, we willconsider the problem of reliable controller design for interval switched systems with time-varying delay. Using Lyapunov method, a new way of designing reliablecontroller can be obtained.In the last section of each chapter, some practical numerical examples are used toverify the results presented are correct, effective and less conservative. In addition,some plans in future should be given.