The Stabilization Of Complex Switched System

The paper maining studided a kind of mixed system-switched system, which has important significance in practical engineering application. Usually, it is composed of a series of subsystems and the corresponding switching rules. Every subsystem can become an independent system model by switching rules. For switched systems, the stability is the most basic requirement, but also the focus of research in the field of control. But in practical engineering, widespread lag and uncertainty factors, often lead to system instability or the system performance decline. Therefore, the study of uncertain switched systems with time-delay stability has very important significance. With the continuous research of switched systems, more and more scholars begin to begin in the study of the stability of switched systems with time delay, in order to make the results more conservative, through unremitting efforts, eventually won the ideal result. In recent years, there have been many new ideas and methods for the study of switched systems with time delay. These results have been improved on the basis of the original, but still relatively conservative. In this paper, we study the two kinds of switching systems, and analyze the stability of these two systems:First, the stability of a class of discrete-time switched systems is investigated. Firstly, the asymptotic stability of the system is obtained by using the multi Lyapunov function and the average dwell time method for nonlinear discrete-time switched systems. The result is a sufficient condition for it. Then, the structural modal dependence of the average dwell time is controlled to ensure the exponential stability of the closed-loop system for linear switched systems. Finally, an example illustrates the correctness of the theory.Second, a class of continuous switching systems is investigated. First, construct a corresponding positive common Lyapunov Krasovskii function, system is obtained by means of MDADT method is a with the stability theory of new meaning, in MDADT method based and deal with the control problem of delay SPLSs time stability of the asynchronous L1, that can ensure the sufficient conditions for the exponential stability of the closed-loop system.