Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays

In this paper, the global asymptotic stability analysis problem is investigated for a class of stochastic bi-directional associative memory (BAM) networks with mixed time-delays and parameter uncertainties. The mixed time-delays consist of both the discrete and the distributed delays, the uncertainties are assumed to be norm-bounded, and the neural network are subject to stochastic disturbances described by a Brownian motion. Without assuming the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and some new developed techniques to establish sufficient conditions for the stochastic delayed BAM networks to be globally asymptotically stable in the mean square. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs) that can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.