Study On The Stability Of Totally Positive Differential System

When studying the stability problems of totally positive differential systems,the classical stability theory method can be used to study the stability conclusions of totally positive systems and their totally positive switched systems under different conditions.The most important step is to used stability The theory chooses the appropriate Lya-punov function.For a totally positive system,the application of a composite system is mainly considered.For a totally positive switching system,combining the char-acteristics of the totally positive system and the switching system,considering the average residence time(ADT)switching,choose multiple linear copositive Lyapunov function(MLCLF)and common linear copositive Lyapunov function(CLCLF),so as to study the totally positive switching system stability under the continuous time state and discrete time conditions.In addition,in the real world,many physical and biological systems will involve the relevant properties of totally positive systems or totally positive switching systems.The main research contents and innovations of this paper are as follows:The first chapter describes the research background of this article.Firstly,it introduces the development of totally positive systems and switched systems,as well as the method of dealing with stability problems;then it introduces the definitions and basic properties of totally positive and composite matrices;finally,the definition and basic properties of a totally positive system are introduced.The second chapter studies the stability of totally positive systems.The stability of totally positive systems with time delay is introduced first;then the composite dynamic system is introduced,and the conclusion of the asymptotic stability of the composite system is obtained through the stability theory criteria.It is shown that in the composite case,there is a certain asymptotically stable relationship between the original system and the composite system;finally,numerical examples are given to prove the validity of the conclusion.The third chapter studies the stability of a completely positive switching system.First consider the totally positive switching system under continuous time under ADT switching,choose MLCLF to iterate through the derivative inequality,the system is exponentially stable,and choose CLCLF to get the system to be exponentially stable under arbitrary switching;then consider the totally positive switching system in discrete time under ADT switching and arbitrary switching,choose MLCLF and CLCLF Iteratively reduce and iterate through the inequality,the system is exponentially stable;finally,provide two examples were used to verify the accuracy and feasibility of the method.