Delay-Dependent Approaches to Globally Exponential Stability for Recurrent Neural Networks

This brief deals with the stability analysis problem for recurrent neural networks with delay. An improved stability condition is derived to guarantee the existence of the unique equilibrium point and its globally exponential stability, which is shown with novel methods. Both delay-dependent and delay-independent stability conditions are obtained. Expressed in terms of LMIs, they can be checked using the numerically efficient Matlab LMI toolbox. Examples are provided to demonstrate the effectiveness and the reduced conservatism of the analysis results.

I. Introduction

In THE PAST few years, RNNs have been extensively investigated for their applications in signal processing, pattern recognition, associative memory, optimization problem, and other engineering and scientific areas [1]–[3]. Since delays often occur in the implementation of RNNs and may induce instability and oscillation, stability analysis of RNNs with delay has attracted many researchers and a lot of results on this topic have been reported in the literature, see, e.g., [3]–[7] and reference therein. Some of the results have been recently extended to RNNs with distributed delays or Markovian jump parameters [8]–[11].