Time Varying Delay With Integral Term Stability Analysis Of Neutral Systems

Time delay exists widely in various practical systems,such as nuclear reaction systems,biological systems,engineering chemical systems,population dynamics models and so on.Many such systems are unstable,and the cause of the instability is caused by time delay.In this thesis,we analyze the stability problem of a class of neutral systems and a class of singular neutral systems with time varying delay.For with integral time-varying delay neutral system stability,take the main tool is choosing appropriate Lyapunov-Krasovskii functional and the derivative along the direction of the trajectory is less than zero,can make the stability to achieve relatively good effect.For singular neutral systems,the stability of the system is transformed into a neutral system with constant time delay.Then the LMI functional is selected and the system is designed to control the whole neutral system and ensure the stability of the system.This thesis is divided into six chapters as follows:Chapter 1.Introduction.The stability of neutral delay systems and neutral delay systems are briefly introduced,and the research background and main work of this thesis are presented.Chapter 2.Preliminaries.Mainly introduce some basic knowledge related to the topic of this thesis.Chapter 3.Stability analysis of a class neutral systems with time varying delay and integral term.The main tool in this chapter is to select the effective Lyapunov-Krasovskii functional,to construct the LMI(linear matrix inequality)in the process of analysis,to achieve the purpose of controlling the whole neutral system and ensuring the stability of the system.Chapter 4.The stability analysis of a class of neutral systems with integral terms with integral terms.This chapter is based on the third chapter,and the stability of the system is obtained by using lemma 4.1.Chapter 5.The stability analysis of a class of singular neutral systems.The main idea of this chapter is to transform the singular neutral system into a neutral system with time delay by means of suitable transformation,and then the stability analysis is carried out.The stability of a class of singular time varying delay neutral systems is further analyzed.Chapter 6.Summary and Outlook.Review the research system,method and problems in this thesis,and look forward to the future development of research.