The Stability Analysis Of Two Classes Of Neural Networks With Delays

In this paper, stability of two classes of neural networks with delays was discussed. In chapter two, almost sure exponential stability and pth moment exponential stability of stochastic Hopfield neural networks with continuously distributed delays was investigated. The sufficient condition to guarantee the almost sure exponential stability and the pth moment exponential stability of an equilibrium solution was given by using the Lyapunov function and the nonnegative semimartingale convergence theorem. In chapter three, global robust uniformly asymptotic stability of the equilibrium point for a class of bidirectional associative memory neural networks with time delays and impulses was studied. Firstly, existence and uniqueness of the equilibrium point for it under the robust conditions was studied by using topological degree tool, homotopic invariance theorem and M-matrix. Based on the results, new sufficient conditions were obtained for the global robust uniformly asymptotic stability of bidirectional associative memory neural networks with time delays and impulses by employing suitable Lyapunov functionals and linear matrix inequality approach.