Research On The Stability Of Switched Positive Systems

Switched system is a hybrid dynamic system that controls switching between different subsystems in continuous(or discrete)time,and it is more difficult because of its higher complexity.Because of its high complexity,it is also difficult.The reason is not difficult to find,because the switched system has the characteristics of uncertainty and time delay,at the same time,it depends on the switching rules and the interaction between subsystems to operate,so it is more difficult to control it,which leads to many limitations in practical research.From the analysis of the actual situation,most systems are in non negative state,so the concept of positive system comes into being,that is,when the initial state and input of the system are not negative,the actual state and output are not negative at the same time.The so-called linear switched positive system must conform to the properties of switched system and positive system at the same time.According to Lyapunov stability theory,this paper analyzes the robust control problem of a class of linear switched positive systems with input and state delays,and makes the following innovations: Under the premise of studying the linear copositive Lyapunov functional method,the sufficient conditions for asymptotic stability of discrete-time switched positive systems are obtained.For linear continuous and discrete-time switched positive systems with time delays,the robust control problem is solved directly The design idea of the former controller is applied to the latter,and then the stability problem is discussed in depth.In addition,based on the theory of Lyapunov stability and average dwell time,the weighted L1 gain observer is introduced into the analysis of linear switched positive systems with time delay.Then the effectiveness of the observer is verified by numerical simulation.Finally,it is proved that the gain controller can not only stabilize the original system,but also has good interference suppression ability,which has significant application value.Based on the stability of switched positive system,this paper carries out in-depth research and analysis,and comprehensively discusses the stability of continuous /discrete-time linear switched positive system,which lays the foundation for the development of practical application.Therefore,this research has certain theoretical significance and practical value,which can be used for reference in related fields.Firstly,switched system,positive system and switched system with time-delay are summarized and then basic knowledge,theorem and lemma of two kinds of linear switched positive systems in the stage of stability exploration are discussed so that the follow-up research and exploration can be sufficiently supported and the research work can be more scientific and perfect.In this paper,an average dwell time method is applied to process continuous-time linear switched positive system.The linear copositive Lyapunov function is determined and the stability condition is made clear by switching the average dwell time and simultaneously,conclusions like correlation stability of the positive system are applied to study the linear switched positive system with time delay.Based on the linear copositive Lyapunov function,the average dwell time switching signal is introduced with the aid of the forward model to make clear the sufficient conditions for exponential stability of the discrete switched positive system,and then based on the linear copositive Lyapunov function,another sufficient condition is defined.Regarding discrete switched linear positive system with time delay,some necessary and sufficient conditions for the global asymptotic stability of the system equilibrium point and the existence of switched linear co-positive Lyapunov function are established by switched linear copositive lyapunov function.