The Stability Of Linear Switched Positive System

Switched system is a kind of hybrid dynamic systems which is controlled by the continuous time subsystems or discrete time subsystems and subsystem to switch. Switched system has a greater difficulty and complexity to other types of system. Because the switched systems not only have uncertainty and time delay phenomenon, and switched systems are switched rules with interaction between subsystems and running, so switched systems with greater difficulty. In life, there are a lot of the state of the system are negative, this is the concept of positive system come into being, when the initial condition and the input is negative, the state of the system and the output is also such a system of negative. For a linear switched system, it should meet the nature of the switched system. There are a lot of widely used this kind of system.In this paper, we study the stability of the linear switched system. In this article, we get the linear switching conditions for the stability by Lyapunov and linear matrix inequality. The first chapter of this article presents the definition of linear switched system, research field, the current development and the practical significance of the application system. The second chapter linear switched system is given by some methods of stability analysis. The third chapter, study the stability of the continuous-time linear switched system is a problem by the method of average residence time average resident time switch, conditions for the robust stability of the system are put forward. The fourth chapter mainly research system with time-delay switched linear stability problem. For linear delays switched system, this type of system is usually divided into continuous and discrete time switched linear system. This chapter mainly studies on the stability of the continuous time delay linear switched system. By asymptotic stability and exponential stability properties and conclusion to discuss the stability of the time-delay linear switched system.At the end of each chapter, a numerical example is given to verify the validity of the results, the accuracy and feasibility.