A Class Of Distribution Of The Robust Stability Of Neural Networks With Delay

Since cellular neural networks were proposed,they have advanced with exceptional speed. For their great effectiveness on associative memories,optimal computation,automatic control, etc.,the qualitative analysis of cellular neural networks fixes a large number of experts' attention. By using Lyapunov stability theory,linear matrix inequality(LMI) technique,this paper discussed the delay-dependent global stability of cellular neural networks with distributed time-varying delays,including global asymptotic stability,robust stability.The results what we give are easy to realize in Matlab.Therefore,our work has preferable significance of theoretical instruction.The paper is divided into four chapters:In the first chapter,the background and necessity for the study of the neural networks are presented.Then,some known results of the neural networks with delays are introduced.And the main work of this paper is also simply introduced.In the second chapter,the notations and lemmas needed in the paper are listed.And the Lyapunov stability theory is introduced.In the third chapter,we consider the delay-dependent global asymptotic stability of the cellular neural networks with distributed time-varying delays,by using Lyapunov stability theory and linear matrix inequality(LMI) method,constructing appropriate Lyapunov-Krasovskii function,a new sufficient condition is derived for the global asymptotic stability and the existence of the equilibrium point is proved.In the forth chapter,by using Lyapunov stability theory,convex optimization theory and linear matrix inequality(LMI) technique,a new delay-dependent robust asymptotic stability criterion of the cellular neural networks with distributed time-varying delays is derived.This result has reduced the limiting conditions to the activation function in the networks model greatly.