Stability For Linear Neutral And Retarded Type Distributed Parameter Systems LMI Approach

State space of distributed parameter control systems is an infinite dimensional space, the state of the systems in every moment is a function, Application of distribution param-eters control systems is more wide, research in the use of the mathematical tools is more complicated. In recent years, the distributed parameter control systems theory has become one of the most active fields in the theory and obtain many achievements. These results in engineering system(such as thermal engineering, chemical engineering, aerospace engineering and machine People engineering, etc.), biological and environmental system, economic sys-tem and social system(such as population system)has important significance. Because there exists delay phenomenons in automatic control、chemical industry and electronics system, therefore, dynamical system research with delay has increasingly drawn people’s interest. The method of stability research for linear neutral system is mainly Lyapunov functional method.Combining these points, this paper discusses linear neutral and retard type distributed parameter systems, by LMI (linear matrix inequality) method,stability for linear neutral and retard type distributed parameters are discussed.This paper is divided into three chapters, the main content is as follows:The first chapter is introduction, mainly introduces the background of distributed pa-rameter systems at home and abroad and the content of this article.The second chapter mainly introduces the use of some of the basic concept and basic theory.The third chapter is to discuss system stability.The main results are as follows:Theorem3.1Using LMI method, the selection of the suitable Lyapunov-Krasovskii functional, obtained the linear neutral system stability. Theorem3.2is the controlled output item of systems y(t)=Ex(t), modified as feedback controller u(t)=Ex(t), and the same method to analyse the stability.Theorem3.3is stability analysis for linear retard type system with the same method, had two corollary.The fourth chapter, a three dimensional heat equation example is showed the results of this paper.