Several Types Of Study Of Stability Of Impulsive Differential Systems

This thesis mainly studies stability of several kinds of impulsive differential systems.It is consisted of six chapters.As the introduction,in Chapter 1,the background and history of impulsive differential equation and impulsive functional differential systems,and the main results of this work are stated.In Chapter 2,we discuss the weak exponential asymptotic stability of differ-ential systems.By using Lyapunov function,we get a broader theorem of zero solutions's weak exponential asymptotic stability.In Chapter 3,we consider a class of impulsive functional differential systems.We generalize the weak exponential asymptotic stability for impulsive differential systems with delays via the method of Lyapunov functionals.In Chapter 4,we further investigate the weak exponential asymptotic sta-bility of impulsive functional differential equations.By employing the Lyapunov functions and the Razumikhin technique,some new conditions ensuring the weak exponential asymptotic stability are obtained.In Chapter 5.we deal with the the stationary oscillation problem for a class impulsive interval neural networks with kernel functions,the discrete time-varying delays and infinite delays as well as impulses,impulse is not only related to the moment of t,but also influenced by the moment t-?.By employing Lyapunov functional method and inequality analysis,we present several new conditions which guarantee the stationary oscillation of the addressed interval neural networks with kernel functions and delays as well as impulses.In Chapter 6,we summarize the full thesis and pointed out the further re-search work.