The Study On Control Method Of Switched System

Generally speaking, the switched system is a hybrid system that is composed of a family of continuous-time and discrete-time subsystems and a rule orchestrating the switching between the subsystems. The control studies of the switched system can resolve the stability of a part of the particular systems to a large extent,and there is the theoretical significance and the practical value to study the switched system.This article aims to research an approach to see whether it can makes the given N-dimensional linear system stable by changing switching law. The paper made the two-dimensional linear switched system as my main research object, and divided arbitrary state space of the two-dimensional linear system into two areas, which is called trended equilibrium point and inverted equilibrium point. On this basis, the paper analyzed whether this two-dimensional linear switched system can choose proper switching law to make it stable by the areas. The specific content is completed as followings.(1) The paper researches the stability of the N-dimensional linear switched system.Firstly, the paper applied some knowledge, such as the theory of linear algebra, the theory of matrices,and phase diagram,and we can gain some sufficient conditions that can judge stability of the N-dimensional linear system from this paper by switching. Secondly,for the N-dimensional linear switched system, the paper studies to find a proper switching law that can make it stable, and the paper succeeded in doing that in detail. Finally, the paper proves that three-dimensional switching system can also be used to judge the issue which is about the stability of the system.(2) The problem of control for a class of switched uncertain descriptor systems with time-delay is considered. By means of Lyapunov function, theory of linear algebra and linear matrix inequality (LMI) tools and based on multiple Lyapunov function techniques,a delay-dependent sufficient condition is deduced such that the solution of the switched descriptor system with time-delay is robustly asymptotic stable for all admissible un-certainties under an appropriate switching law. And the corresponding method of the controller's design is given. Furthermore,a convex optimization problem with LMIs constraints is formulated such that the maximum upper bound on the admissible delay can be determined by using the LMI toolbox in Matlab. Finally,an illustrative example is given to demonstrate the effectiveness of proposed method.