Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks With Time-Varying Delays

This correspondence provides stochastic exponential stability for Markovian jumping bidirectional associative memory neural networks with time-varying delays. An approach combining the Lyapunov functional with linear matrix inequality is taken to study the problems. Some criteria for the stochastic exponential stability are derived. The results obtained in this correspondence are less conservative, less restrictive, and more computationally efficient than the ones reported so far in the literature

I. Introduction

The bidirectional associative memory (BAM) neural networks, first proposed and researched by Kosko [1], [2] for their useful application in pattern recognition, solving optimization problems, and automatic control engineering, are a class of two-layer heteroassociative networks with and without axonal signal transmission delays. The stability of the equilibrium points ensures the stored memory can be retrieved. Therefore, the investigation on the stability of a BAM network has been the highlight in this field. The stability of this type of network has been extensively studied. In [3]–[12], by using the method of the Lyapunov functional, a lot of sufficient conditions have been given ensuring the stability of the BAM neural networks with delays. The stability criteria of delayed BAM neural networks with impulses or reaction-diffusion terms or distributed delays are derived, and we refer to [8], [11]–[17], and the references cited therein for more details.