Global exponential stability and periodicity of CNNs with time-varying discrete and distributed delays

Abstract

In this paper, based on the Lyapunov stability analysis for functional differential equations, the problems of global exponential stability and periodic solutions for a class of cellular neural networks with time-varying delays and distributed delays are investigated. By constructing a new suitable Lyapunov functional, some simple sufficient conditions ensuring existence, uniqueness, global exponential stability of the equilibrium point and periodic oscillation of the networks are obtained, which are easy to check and apply in practice. In addition, an example is also given to illustrate the effectiveness of the theory. © 2008 Springer-Verlag Berlin Heidelberg.