Analysis And Synthesis Of Interconnected Positive Systems On Time Scales

Interconnected systems are a kind of composite systems which composed of a series of subsystems connected to each other in a specific way.In recent years,interconnected systems are widely used in aerospace,power system,urban transportation network,digital communication network,ecosystem and so on.So many scholars have devoted themselves to the study of interconnected systems.Scholars have researched a lot on the stability and control of interconnected systems.But there are few researches of the stability and controller of interconnected systems on time scales.Therefore,this paper will focus on a class of interconnected systems with special structure on time scales.The thesis is divided into five chapters:In Chapter 1,this paragraph mainly introduces the research background,current situation analysis and lists some basic theoretical knowledge.In Chapter 2,the paragraph studies the L₁-gain question of the positive system with weighting vectors on time scales.Based on the definition of induced norm with weighted vectors,this chapter gives the L₁-gain condition with weighted vectors of the system,and verifies the validity of the conclusion by numerical examples.In Chapter 3,this part investigates the positivity and stability issues of intercon-nected systems on time scales.The positivity condition of interconnected systems are given at first.Then,based on the conclusion of chapter 2,the stability condition of interconnected systems is given by using linear programming method and so on.Next,this chapter studies the stability of the interconnected systems under the permutation matrix connection problem.Finally,this chapter introduces the stability condition of interconnected systems with two subsystems,and verifies the effectiveness of conclusion by numerical example.In Chapter 4,this paragraph mainly discusses decentralized feedback controller design problem of the interconnected systems on time scales.At first,based on the interconnected systems stability theory,this chapter gives the design method of decentralized feedback controller for the interconnected systems which do not meet the stability conditions by using the L₁induced with weighting vectors norm as a performance criterion,and gets the necessary and sufficient condition which make the closed-loop system asymptotically stable.Then,for the interconnected systems which cannot be measured directly,this chapter gets the sufficient and necessary conditions which make the error systems meet certain performance indicators by designing a decentralized observer.And the chapter gives numerical example to verify the validity of the conclusions.In Chapter 5,the paragraph summarizes the whole thesis and makes further prospect for the future work.