The Stabilization Of Positive Switched Systems

The positive system is a kind of system which is very common in reality,such as population model,economic development model and so on.It is a kind of dynamic system with the state and the output of the system is always nonnegative when the initial condition and the input are nonnegative.As an indispensable hybrid system,the switched system has a good application in computer room management,traffic system,power system and so on.It is composed by subsystems and switching laws.Positive switched system is a kind of system which is composed of a finite number of positive subsystems and a switching signal.Over the past ten years,positive switched system has attracted more and more researchers' attention in the field of communication,medical treatment,automation and so on.According to the role of the switching system in different applications,it should be in accordance with the nature of two points,positive and having switching law.It should be pointed out that the research on positive switched system in many problems has great challenge compared with the two systems mentioned above.The research is carried out from the following aspects:The first chapter is survey.It discusses the significance of the research on the positive switched systems,and summarizes some main problems and current situation of the research on the positive switched systems.In combination with some theoretical problems of positive switched systems,such as stability,stabilization,observation,etc.According to these problems,this paper introduces the research methods of positive switched system.At last,the main content and framework of this paper is introduced.In the second chapter,the problem of robust stabilization for positive switched systems with polytopic uncertainty is discussed.Firstly,the stabilization problem of the positive switched systems with polytopic uncertainty is discussed by using multiple linear copositive Lyapunov function method.Secondly,based on the linear programming method,the sufficient conditions for the global exponential stability of the positive switched systems with polytopic uncertainty are given,and the state feedback control law is designed to solve the stabilization problem of the positive switched systems with polytopic uncertainty.Finally,the simulation case is given to declare the effectiveness of the proposed method.In the third chapter,improved controller design for positive systems and its application to positive switched systems is studied.By decomposing the feedback gain matrix into parts,a new controller is designed,and the new system feedback control law is constructed.The rank of the gain matrix is no longer limited to 1,which reduces the conservatism of the conclusion.At the same time,the system is both positive and stable.Finally,the effectiveness of the proposed method is verified by simulation.In the fourth chapter,the l₁-gain analysis and the robust stabilization of positive switched systems are studied.A sufficient condition for the stabilization of the system based on the average residence time is established through the use of Lyapunov function.At the same time,the feedback control law which makes the system global exponential stable is given,and the 1gain is obtained.Finally,examples are given to test the feasibility of the proposed method.The fifth chapter is the summary and prospect.First of all,this paper summarizes the important conclusions of this paper.Secondly,it puts forward the problems that may be studied in the future.