Improved conditions for global exponential stability of recurrent neural networks with time-varying delays

This paper presents new theoretical results on global exponential stability of recurrent neural networks with bounded activation functions and time-varying delays. The stability conditions depend on external inputs, connection weights, and time delays of recurrent neural networks. Using these results, the global exponential stability of recurrent neural networks can be derived, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail.

I. Introduction

Since hopfield's inspirational work on stability of the Hopfield neural network (HNN) using energy function [1], numerous studies on the stability of various neural networks have been reported. The stability properties primarily concerned are uniqueness, global asymptotic stability, and global exponential stability of equilibria. In recent years, the stability analysis of recurrent neural networks (RNNs) with time delays received increasing attention, e.g., [2]–[21].