Robust Stability And Robust H_∞ Performance Analysis Of Multidimensional Uncertainty Sampling System

Due to the use of the aspects of numerical control system and the network control system, the sampled-data system has received extensive attention. With the actual use of network numerical control system, the sampled-data control system also exists in all kinds of practical technology, such as the production of digital electronic computer,digital computer parts production, and so on. Considering the actual sampled-data control system will inevitably exist uncertainty, such as polyhedron uncertainty,norm bounded uncertainties,linear uncertainty and so on. However we also use the robust control theory to deal with the uncertainty of the system. So studying the uncertainty of the sampled-data system robust stability and robust H?performance has very important theory significance and practical value. In this article we mainly discuss polyhedron uncertainty of sampled-system robust stability and robust H?performance.In recent years, we usually study the sampled-data control system robust stability by using the discretization method that transforms sampled-data systems into discrete-time systems and another approach that the sampled-data systems were represented in the form of an impulsive model. In this article, We will make the sampled-data system and its uncertainly into time-delay systems to study its robust stability.In other words, In the framework of the input delay approach, the sampled-data system is converted into continuous system with input delay in this article, then we use the existing control theory and the Lyapunov functional method with the help of Jensen’s Inequality、Descriptor method and the property of the linear matrix inequality at the same time, we will draw a sampled-data system stability conditions in the form of linear matrix inequality, and then on the basis of the uncertainty of sampled-data system stability conditions are obtained. Finally,compared with the existing results, the example simulation results prove the validity of the result.This article is divided into five chapters.In chapter one, we introduce the background of the research and the content of the stability for sampled-data systems. On this basis, we illustrate the main content of this article.In chapter two, we mainly introduce the theoretical knowledge which in neededby the article, such as the LMI methods, Lyapunov stability theories, and some important lemmas. The main purpose is for this paper smoothly does.In chapter three, based on the second lemma, and using Lyapunov functional method, the asymptotic stability of the sampled-data system is given in the form of LMI conditions.then we conclude the theorem 1. At the end of this chapter, by using LMI toolbox, we carried on the simulation. The result we obtained show that the better conservatism of the theoretical results than the present results.In chapter four, we put the asymptotic stability of the sampled-data system of the chapter three promotion to the polyhedron uncertainty sampled-data system. The main task is to analyze the H?performance of the polyhedron type uncertainty sampled-data system, and the main basis is Lyapunov functional method, Jensen’s Inequality 、 Descriptor method and the thinking methods of convex optimization.Finally, the simulation results prove the effectiveness of the conclusion.In chapter five, the content of the paper is summarized, and the problems which will be studied in the future are prospected.