Analysis And Synthesis Of Stability And L_? Performance Of Positive Systems With Time Delay On Time Scales

In engineering theory and practice,it is difficult to describe the mathematical mod-el of actual systems only by using continuous-time and discrete-time systems,so more and more scholars begin to devote themselves to the research of continuous and discrete systems or even more complex time scale systems.In this paper,we will investigate the dynamic properties of positive systems with time delay on time scales.The full text is divided into five chapters:In chapter 1,we mainly introduce the research background and main tasks,then lists some preliminaries related to this paper.In chapter 2,the stability and L?-gain of time-varying delay positive systems on time scales are mainly studied.We take bounded time-varying delay positive systems and unbounded time-varying delay positive systems as research object,and give the conditions of positive and stability for time-varying delay positive systems on time scales.Then,we discuss the L?-gain of these systems based on comparison principle and concluded that the L?-gain of these systems satisfies time-delay independence criterion.In chapter 3,we mainly investigate the design of positive observer for positive systems on time scale.Based on linear programming method,the existence conditions and design methods of observer for positive systems and uncertain positive systems are given;Then,the feedback stabilization of positive observer for positive systems is discussed.In chapter 4,the design of positive observer for positive time-delay systems on time scales is mainly studied.By transforming this problem into linear programming problem,we study the existence conditions and specific design methods of observer for positive time-delay systems and uncertain positive time-delay systems.Then,the feedback stabilization of positive observer for positive time-delay systems is also discussed.In chapter 5,the conclusions are summarized and the further research is prospected.