Robustness analysis of a class of discrete-time recurrent neural networks under perturbations

A robustness analysis is conducted for a large class of discrete-time recurrent neural networks for associative memories under perturbations of system parameters. The present paper aims to give an answer to the following question. Given a discrete-time neural network with specified stable memories (specified asymptotically stable equilibria), under what conditions will a perturbed model of the discrete-time neural network possess stable memories that are close (in distance) to the stable memories of the unperturbed discrete-time neural network model? Robustness stability results for perturbed discrete-time neural network models are established and conditions are obtained for the existence of asymptotically stable equilibria of the perturbed discrete-time neural network models which are near the asymptotically stable equilibria of the original unperturbed neural networks. In the present results, quantitative estimates (explicit estimates of bounds) are given for the distance between the corresponding equilibrium points of the unperturbed and perturbed discrete-time neural network models considered herein.