Stability Analysis Of Neural Networks With Time Delays

Neural network(NN)has been successfully applied in engineering and scientific areas.How-ever,in the process of the physical implementation of artificial NNs,the time-delay is objective existence,which might cause oscillation,divergence,and even instability.Therefore,the stability of the neural networks with delay(DNNs)has attracted worldwide attention.This article focuses on the asymptotic stability for a class of generalized DNN,which is based on Lyapunov stability theory and linear matrix inequality(LMI)methods,and new stability results are given.More specifically,the main contents of this article are as follow:Chapter 1 reviews the history of NN,the present study situation of the stability for DNNs,and at last simply introduce the main content of this article.Chapter 2 gives the system model of the generalized DNN,and the Lyapunov stability theory and LMI methods are introduced simply.Moreover,some related lemmas are given,which are used in the process of the proof.Chapter 3 analyzes the asymptotic stability of the generalized delayed neural network.Firstly,a new candidate Lyapunov functional with more information of the activation function is defined.Then,introducing a new integral inequality to estimate the derivative of the Lyapunov functional and a new asymptotic stability condition is obtained by Lyapunov stability theory.Finally,two examples are listed to illustrate the stability result,which is less conservative than some recently reported ones.Chapter 4 further analyzes the asymptotic stability of the generalized delayed neural network.Firstly,based on the Lyapunov functional of Chapter 3,an improved Lyapunov functional is con-structed.Then,its derivative is estimated by integral inequality and reciprocally convex combi-nation lemma reported recently,and an improved asymptotic stability condition is obtained by Lyapunov stability theory.Finally,the simulation results of two examples show the improvement of the conditions in this chapter.Chapter 5 summarizes the main work of this paper,points out the possibility of further reduc-ing conservative and indicates the direction for further work.