Stabilization And Stability Analysis Of Switched Positive System

Positive system is a kind of common system in real life.When the initial conditions and input are non-negative,the dynamic system whose state and output are always non-negative is called positive system.The switched system is also an important research system in hybrid dynamic system,which is composed of several subsystems and a control subsystem switching logic rules.Switched positive system is a system composed of a limited number of positive subsystems and switch signals.Over a longer period of time,switched positive system has attracted more and more researchers' attention in the range of communication system,medical treatment,intelligent transportation and so on.Because of the extensive engineering background of the switched positive system,the theoretical research on it is also of great significance.In this paper,the stability analysis and stabilization of several switched positive systems are studied.The main contents are as follows:The first chapter is the introduction.This paper mainly discusses the research background and significance of the switched positive system,and summarizes the research status of some researchers on the switched positive system.For example,stability,stabilization,etc.Secondly,it briefly introduces some basic knowledge needed in this paper.The second chapter studies the stabilization of the continuous time switched positive system.Based on the method of linear copositive Lyapunov function and the designed switching rules,the stabilization of the switched system is discussed.Finally,the validity of the method is verified by numerical simulation.The third chapter discusses the stabilization of discrete-time switched positive systems.By designing time-dependent switching rules and combining the Lyapunov function,the system studied is asymptotically stable.Finally,simulation examples demonstrate the effectiveness of the method.The fourth chapter addresses the diagonal exponential stability problem of a class of nonlinear switched systems with delays.By using the homogeneous polynomial Lyapunov function method,a diagonal exponential stability condition is proposed for a positive linear system serving as the comparison system of the original nonlinear system.A relationship between trajectories of the comparison system and the original one is then revealed,resulting in a simple condition to determine the diagonal exponential stability of the original nonlinear system.Two numerical examples provided herein to illustrate the theoretical calculation results obtained.