Stability Analysis And Application Of Impulse Proportional Delay Differential System

This master paper investigates the stability of differential systems with impulses and proportional delays and its applications in neural networks.We will discuss the stability of impulsive proportional delay differential systems in two cases of persistent impulsive perturbation and impulsive control,and moreover,analysis the stability of a class of impulsive cellular neural networks with proportional delay.This paper consists of four chapters:The first chapter introduces the purpose and significance of the research and related research status.The second chapter discusses the problem of persistent impulsive effects on stability of the general differential systems with proportional delay and variable coefficients.First,By presenting a new Razumikhin condition and applying Lyapunov-Razumikhin method,sufficient conditions are obtained to guarantee the global power stability of the zero solution of the addressed system.Second,as an application,several global power stability conditions are derived for a class of cellular neural networks with proportional delay and persistent impulses.Finally,two examples are provided to show the effectiveness of the obtained results.In the third chapter,from impulsive control point of view,we discuss the problem of stabilization of the general impulses differential system with proportional delay.First,some delay-dependent conditions are established to guarantee the stabilization of the zero solution of a impulsive differential system with proportional delay by employing the Lyapunov function method and some improved Razumikhin techniques.Second,based on the obtained criteria and LMI approach,several delay-dependent conditions are derived to ensure the uniqueness and global asymptotic stability of the equilibrium point of a class of cellular neural networks with impulses and proportional delay.Finally,we give three numerical examples to demonstrate the feasibility of the obtained results.Chapter four is the summary and prospect of our paper and introduces some problems in the next works.