Stability Analysis Of Nonlinear Switched Systems

The behavior of switched systems is very complicated because of the interaction between the continuous dynamics and discrete switching signals.This provides new areas of research and challenging problems in information sciences,control sciences and related fields.Meanwhile,research results of switched systems also make significant reference to general hybrid systems in terms of ideas,methods and theories.Therefore,the study of switched systems has great academic value and significant applications. In this dissertation, the problem of exponential stability and robust H_∞control of a class of nonlinear switched systems with time-delay and disturbance is mainly studied. The sufficient condition for quadratic robust stabilization of a class of nonlinear discrete-time switched systems is given in the last. Corresponding adopted study methods are Lyapunov function method, differential inequality method. These methods combine with LMI to deal with the problem on exponential stability and robust H_∞control problem.The arrangement of this dissertation is as follows.In chapter 1, conception of hybrid systems, recent development, study methods and application fields of switched systems are introduced. The preface generalizes the basic theory of stability, derives the meaning of investigating stability for switched systems, and sums up the central content of the paper.In chapter 2, a class of nonlinear switched systems with time-delay model is discussed. By using Halanay inequality, variation-of-constants formula and differential inequality method, sufficient conditions of exponential stability for the nonlinear switched systems with time-delay are obtained.In chapter 3, the problem of robust H_∞dynamic output feedback stabilization for nonlinear switched systems with time-delay and disturbance is considered on the base of linear switched systems theory. By using LMI method and Lyapunov function, sufficient conditions of robust stabilization and H_∞performance for the system are obtained. Robust H_∞dynamic output feedback controllers are designed.In chapter 4, Basing on LMI and H_∞control theory, by constructing a linear matrix inequality using Schur complement formula and Lyapunov function method, a sufficient condition for the H_∞quadratic stability of a class of nonlinear switched system with time-delay and disturbance is presented to solve certain linear matrix inequality.In chapter 5, the whole dissertation is summarized. Work assumption in the future and the direction of endeavor are pointed out.