Stability Analysis For Several Classes Of Systems With Time-varying Delays

The time-delay phenomenon often exists in the social life and real systems, suchas specialized production system, neural network system, biologies system and so on.The existence of time delay is an important factor that makes the systems unstable andbad systems performance. Therefore, the study of stability problem of time-delaysystem attracted the attention of the experts and scholars and emerged manyoutstanding research results. There are many kinds of systems with time delay anddifferent systems may exhibit different properties, so it has a practical significance tostudy the different types of delay system.This paper mainly study interval time-varying delay systems, nonlinearperturbation system and Lurie system with time delay. By using theLyapunov-Krasovskii stability theory and linear matrix inequalities method, thestability criterion of several typical time-delay systems is obtained.The first chapter briefly introduces the the research status at home and abroad,the significance of the research of interval time-varying system, nonlinearperturbation system and Lurie system with time delay, as well as the main work of thepaper. The second chapter introduces some basic principles, lemmas and concepts.The third chapter studys the stability of interval variable delay system. By conbing thedelay fractioning idea with reciprocal convex technology, this paper obtains thestability criteria for interval time-varying system. The fourth chapter discusses thestability analysis of time-delay systems with nonlinear parameter perturbations.Basing on the basis thought that the delay information are devided into three sectionsand using Jesen inequality method and reciprocal convex technology, this paper getthe better stability criterion. The fifth chapter mainly discusses the stability problemwith Lurie type time-varying delay systems. By dividing the delay information into nparts and using the reciprocal convex technology into the deriviton of theLyapunov-Krasovskii function. This paper obtains the stability criterion. Finally,numerical examples are showing in each chapter for the purpose of indicating that theresults introduced in this paper are less conservative and effective than other papers. This paper summarizes the current development status of time-delay system, andputs forward the future work needed to be further researched.