Stability And Stabilization Of Two-dimensional Linear Time-invariant Switched Systems With Multiple Foci And Centers

This dissertation investigates stability and stabilization issues of two-dimensional linear time-invariant (LTI) switched systems with potentially unstable subsystems and multiple foci and centers. Firstly, for the case that every subsystem has a unique focus or center and these equilibria are different from each other, we determine a unique certain region contained all the equilibria, and then give a new kind of stability concept-region stability. Based on the region stability introduced, by means of the mathematical analysis method we propose several simple region stability criteria for globally asymptotical re-gion stability of two-dimensional LTI switched systems composed of two subsystems with different focus or center. Then, for such switched systems we extend the above region stability results obtained to the case that there are more than two subsystems. Thirdly, global asymptotical region stabilizing controls and corresponding algorithms are designed for such switched systems based on the region stability proposed. Finally, several illustra-tive example and their simulations demonstrate the effectiveness and practicality of the new stability and stabilization results obtained in this dissertation. This thesis consists of four chapters as follows.The first chapter is to give the preliminaries of the studying background and the motivation of this dissertation, some notation and assumptions which will be used in the sequel, and simple introduced the main conclusions of this paper.In the second chapter, switched system stability analysis is carried out for two-dimensional LTI switched systems with multi-equilibria. Firstly, based on the determined unique region, we propose a concept of region stability for such switched systems. Sec-ondly, we present a series of simple and practical sufficient conditions of asymptotical region stability of two-dimensional LTI switched systems composed of two stable sub-systems under specific or arbitrary switching paths, in which switching states are all lie on the switching line contained all the equilibria of subsystems. Then we extend these region stability results to the case that there are more than two subsystems with focus or center for the kind of switched systems. Finally, an example illustrative example shows that the new region stability results obtained are effective and practical.In the third chapter, we investigate the stabilization issues of two-dimensional LTI switched control systems with multiple equilibria. We first introduce a concept of re- gion stabilization of such switched systems, and based on the region stabilization concept proposed and the region stability results obtained in the second Chapter, this chapter proposes several sufficient stabilization conditions for such kind of switched systems. Sec-ondly, based on the obtained region stabilization results, we design globally asymptotical and stabilizing state feedback control laws and their corresponding algorithms. A nu-merical example is also carried out to show the stabilization results are effective and practical.In the fourth chapter, we conclude this thesis, and give some interesting issues that will worth to be studied in the future.