Robust stability for stochastic interval Hopfield neural networks with time delays

In this paper, the robust stability for a kind of stochastic interval delayed Hopfield cellular neural networks is investigated by means of the Itô formula, Razumikhin theorems, Lyapunov function and norm inequalities. several simple sufficient conditions are obtained which guarantee the robust stability of the stochastic interval delayed Hopfield cellular neural networks. some recent results reported in the literature are generalized. Furthermore, that a Remark and a kind of equivalent description of this stochastic interval delayed Hopfield cellular neural networks are also presented.

I. Introduction

In recent years, the study of Hopfield neural networks has attracted considerable attention since it plays an important role in applications such as classification of patterns, associative memories and optimization. To the best of authors' knowledge, in neural processing and signal transmission, significant time delays as a source of instability and bad performance may occur. Therefore, the stability analysis problem of Hopfield neural networks with time-delay has been attracted a large amount of research interest and many sufficient conditions have been proposed to guarantee the asymptotic or exponential stability for the neural networks with various type of time delays such as constant, time-varying, or distributed, see for example, [16], [17], [18], [21]~[25], [27]~[31] the references therein.