Robust stability of discrete-time stochastic neural networks with time-varying delays

Abstract

In this paper, the global exponential stability problem is studied for a class of discrete-time uncertain stochastic neural networks with time delays. The stability analysis problem is investigated, for the first time, for such kind of neural networks. In the neural network model, the parameter uncertainties are norm-bounded, the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion, and the delay is time-varying. By utilizing a Lyapunov–Krasovskii functional and using some well-known inequalities, we convert the addressed stability analysis problem into the feasibility problem of several linear matrix inequalities (LMIs). Different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to establish sufficient conditions for the neural networks to be globally, robustly, exponentially stable. A numerical example is provided to show the usefulness of the proposed global stability condition.