The Stability Analysis And Observer Design For Classes Of Discrete Systems With Time-delay

The discrete systems with time-delay are the main research objectives in thispaper. The stability analysis and the output feedback control based on state observerfor a class of discrete system with multiple time-varying time delays are studied. Inaddition, the stability and output feedback controller for a class of nonlinear discretesystem with time-delay are discussed. State observer and robust observer fornonlinear Lipschitz discrete system with time-delay are designed. The theories ofLyapunov stability, Luenberger-type observer design, linear matrix inequalitytechnique, Lyapunov-like method are the main research methods. The correspondingsimulation examples are given in order to illustrate the feasibility and effectiveness ofsome results in the paper.The main contents summed up as the following five sections.1. The background of this paper and the research overview for district systemwith time-delay are reviewed in this part. The basic theories of stability analysis andobserver design are introduced, as well as the definition and basic method. And thenthe main research works are summarized.2. Stability analysis and observer design problem for the linear district systemwith multiple time-varying delays is researched in this section. Some sufficientconditions for the stability and output feedback stabilization of the system areobtained by using Lyapunov function method and the linear matrix inequalitytechnique. A state observer is designed for the system based on a feedback controller.A sufficient condition is proposed for the output feedback stabilization based on thestate observer. Finally, an example is given to illustrate the effectiveness andfeasibility of the proposed method in Section2.3. The research overview of the stability analysis for nonlinear district system is summarized. Stability analysis of a kind of nonlinear district system with time-delayis researched in this section. A sufficient condition is obtained for the stability of thesystem. Linear output feedback controller and nonlinear output feedback controllerare designed to stabilize the system. At last, an example is given to illustrate theapplicability and feasibility of the researched results.4. The research overview of the observer design for nonlinear district system issummarized. The problem of state observer design for a kind of nonlinear Lipsczhitdistrict system with time-delay is researched in this section. Firstly, a new full orderstate observer is proposed to ensure the error system stable. Secondly, as for thenonlinear Lipsczhit district system with disturbance, the design method of full orderrobust observer and reduced order robust observer is obtained. Finally, theeffectiveness and the feasibility are illustrated for the proposed approached in thischapter by a simulation example.5. All the results of this paper are summed up in this part. And the further studyplan and the outlook are given.