Stability And Stabilization Of Two-Dimensional LTI Switched Systems With Saddle Points

This dissertation investigates the stability and stabilization issues of two-dimensional linear time-invariant(LTI) switched systems with saddle points. For the case that each subsystem has a unique saddle point-zero equilibrium, based on the conception of the Lyapunov stability, a number of sufficient conditions of locally asymptotical stability are obtained for two-dimensional LTI switched open-loop systems with saddle points under almost arbitrary switching lines. Based on the stability results obtained, we obtain several globally asymptotical stabilization results, and design stabilizing con-trol laws and corresponding algorithm for two-dimensional LTI switched closed-loop systems. An illustrative example and its simulations are carried out to show that the stability and stabilization results obtained in this paper are corrective, effective and practicable. 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, and several definitions, some notation and assumptions which will be used in the sequel.In the second chapter, system stability analysis is carried out for two-dimensional LTI switched systems with saddle points. Firstly, based on the special structures of the phase diagram, we propose the specific expression of asymptotes and the concepts of the trajectory direction of the open-loop subsystems, and obtain a criterion of the direc-tion of subsystems of such switched systems. Secondly, without resort to the classical stability analysis methods based on any Lyapunov functions, by means of the criterion of the subsystems’direction and the Lyapunov stability concept, we present a series of simple sufficient conditions of locally asymptotical stability of two-dimensional LTI switched open-loop systems with saddle points under almost arbitrary switching lines. Finally, an example illustrates the correctness, effectiveness and practicability.In the third chapter, we investigate the stabilization issues of two-dimensional LTI switched control systems. Based on the stability results obtained in the second chapter, this chapter first proposes several sufficient conditions of stabilization for such switched systems and then designs globally asymptotical stabilizing state feedback control laws and stabilizing switching lines. Then, this chapter designs the corresponding algo-rithms of the globally asymptotical stabilizing state feedback control laws and stabiliz-ing switching lines developed in this thesis. Finally, A numerical example is carried out to show the stabilization results are corrective, effective and practicable.In the fourth chapter, we conclude this thesis, and give some interesting issues that will worth to be studied in the future.