Region Stability And Stabilization Of Two-dimensional Switched Continuous-discrete Time Linear Systems With Multi-equilibria

This thesis studies the region stability and stabilization of two-dimensional switched linear time-invariant systems with multiple equilibrium points.Such switched systems compose of both discrete-time subsystems and continuous-time subsystems.It is indeed very difficult to study such kind of switched systems.This is because that such a switched system is composed of both discrete-time subsystems and continuous-time subsystems;All the subsystems’ equilibrium points are not just the same one;The shortage of necessary analysis methods/techniques.By using analytical method and matrix series analysis method,this thesis studies four classes of two-dimensional switched discrete-time and continuous-time linear time-invariant systems with multiple equilibrium points as follows.All the subsystems’ state matrices are diagonal matrices;All the subsystems’ state matrices are upper diagonal matrices;All the subsystems’ state matrices are lower diagonal matrices;And all the subsystems’ state matrices are both diagonal matrices and lower triangular matrices.The main research contents and results are as follows.(1)The stability issue is studied for two-dimensional switched continuous-time and discrete-time linear time-invariant systems with multiple equilibrium points.Firstly,according to the following two certain characteristics: The equilibrium points of all subsystems of the switched system are different from each other;And all subsystems have a same dwell time,this thesis determines a specific region containing all the subsystems’ equilibrium points.Then,the general solution of such kind of switched systems is obtained via the iterative method and the mathematical analysis method.Finally,based on the concept of regional stability,some simple criteria of region stability and region asymptotic stability are proposed for the above four types of switched linear time-invariant systems by using the series convergence analysis method.(2)The region stabilization issue is studied studies for two-dimensional switched continuous-discrete linear time-invariant systems with multiple equilibrium points.Based on the results of region stability obtained in this thesis for such kinds of switched linear systems,under the condition that every subsystem is controllable,the globally asymptotic state-feedback region stabilizing controllers are designed for the above four types of switched systems.(3)Numerical simulations.For the four classes of switched systems,several numerical examples are carried out via the soft of MATLAB.The numerical simulations show that the effectiveness and practicality of the theoretical results obtained in this thesis for region stability and region stabilization of two-dimensional switched discrete-continuous linear systems with multiple equilibrium points.