Stability Of Two Kinds Of Impulsive Neural Network Systems

In this paper,we mainly consider the model of variable-time impulsive Hop-field neural network system with piecewise constant argument and time delays.Sufficient conditions are achieved to the stability of solutions by a series of systematic analyses.This thesis is composed of three chapters.In Chapter 1,we introduce the historical background,research status of this article and the main works of this paper.In Chapter 2,we discuss the stalbility of impulsive Hopfield neural network system with piecewise constant argument.In fact wo knw that the time of the pulses are usually not fixed by the system,but change with the change of the solution.Therefore,on the basis of the origimal model,we join the variable time pulses.The main method is to transform the variable-time impulsive system into a fixed-time impulsive system by the B-topology and B-equivalence theory,Brouwer fixed point theorem is used to get the existence of equilibrium solution,and finally,using the method of Lyapunov function and linear matrix inequality(LMI)gets the sufficient conditions of global robust.asymptotic stability of solution.In Chapter 3,we discuss the stability of the time-delay impulsive neural net-work system.The main method is to construct a suitable V function by using the impulsive differential inequality and the generalized Halanay inequality.Then we get the sufficient conditions to guarantee the stability of this system.