The Characterization For The Controllability And Reachability Of Switched Linear System

Controllability and observability are a pair of very important conceptions in the theory of linear system. They provide us with certain structural features of linear system as well as some internal properties of the system, and are essential for certain design problems of system. The paper mainly focus on controllable set and reachable set of switched linear system.Inspired by the fact that a general linear DAEs can be decomposed into a slow subsystem and a fast subsystem, we use the similar method to study the switched system. Our method is to choose an arbitrary subsystem of the switched system, utilize the related knowledge of the Wong sequences and construct the corresponding invertible matrices S and T. In this way, we transform the initial switched system into two subsystems with switching signal. Then based on the theory of the general linear system, we can get the controllable set and reachable set for the switched system by using the similar method.The thesis is organized as follows:Some background knowledge is given in Chapter1. In Chapter2, some related definitions are presented. Chapter3gives some preliminaries. In Chapter4, we choose an arbitrary subsystem of the switched system, utilize the related knowledge of the Wong sequences and construct the corre-sponding invertible matrices S and T. In this way, we transform the initial switched system into two subsystems with switching signal. In Chapter5, characterization for the controllability and reachability of the transformed slow subsystem is presented. In Chapter6, we give some conclusions and discussions.