Stability Analysis Of Switched Positive Systems With Time Delay

This thesis mainly investigate the globally asymptotic stability of discrete-time switched positive systems with arbitrary time delay, and the uniformly asymptotic stability of a specific continuous-time switched positive systems with arbitrary time delay.In chapter 1,we state the background of the problem and the current development of the problem.In chapter 2,we make use of switched copositive Lyapunov functional to study the discrete-time switched positive systems with arbitrary time delay,and obtain some sufficient conditions about the globally asymptotic stability of the origin.At the same time,we obtain some necessary and sufficient conditions on existing a switched copositive Lyapunov functional.In chapter 3,we use common Lyapunov-Krasovskii functional to investigate the continuous-time switched positive systems with arbitrary time delay,and obtain some sufficient conditions about the uniformly asymptotic stability of the origin,together with the necessary and sufficient condition on existing a common copositive Lyapunov functional for switched positive systems,we obtain some easily checking sufficient conditions on the continuous-time switched positive systems with arbitrary time delay.We consider the corresponding discrete-time switched positive systems and obtain some sufficient conditions about the uniformly asymptotic stability of the origin.We give some examples in chapter 2 and chapter 3.