Stability Of Cellular Neural Networks With Delays

This paper studies the stability of the following cellular neural networks :A series of new results are obtained. And some of them improve or extend the related results in the literature.In chapter 1, we introduces the background of the problem-researching and the recent development of the research in this field.In chapter 2, a new sufficient condition is given for the global asymptotic stability of a unique equilibrium point of cellular neural networks (1) with time-varying delays. The sufficiant condition only relies on the feedback matrices and is independent of the delay parameters. Furthermore, this condition is less restrictive than those given in the literature.In chapter 3 , the global exponential stability of discrete-time neural networks with delays is discussed. By the Lyapunov functional method , a sufficient condition is given for the global exponential stability of discrete-time neural network (2).In chapter 4 , a new sufficient condition is given for the global exponential stability of a unique equilibrium point of discrete-time cellular neural networks.By applying the inequality pap xb < (p — l)ap + If, where p denotes a positive integer and a, b denote nonnegative numbers,and constructing appropriate Lyapunov functionals we obtain a set of delay independent and easily verifiable sufficient conditions under which (3) and (4) have unique equilibriums which are .globally exponentially stable, respectively. It is shown that the conditions rely on the feedback matrices and are independent of the delay parameters.