Global asymptotic and robust stability of recurrent neural networks with time delays

In this paper, two related problems, global asymptotic stability (GAS) and global robust stability (GRS) of neural networks with time delays, are studied. First, GAS of delayed neural networks is discussed based on Lyapunov method and linear matrix inequality. New criteria are given to ascertain the GAS of delayed neural networks. In the designs and applications of neural networks, it is necessary to consider the deviation effects of bounded perturbations of network parameters. In this case, a delayed neural network must be formulated as a interval neural network model. Several sufficient conditions are derived for the existence, uniqueness, and GRS of equilibria for interval neural networks with time delays by use of a new Lyapunov function and matrix inequality. These results are less restrictive than those given in the earlier references.

I. Introduction

IT IS WELL KNOWN that a time delay is likely to be present due to the finite switching speed of amplifiers and occur in signal transmission among neurons in the electronic implementation of neural networks, which will affect the stability of neural networks. Beside time-delayed features of such neural networks, there might also be some uncertainties such as perturbations and component variations, which might lead to very complex dynamical behaviors such as oscillations, bifurcation, and chaos, etc.