Robust Stability for Interval Stochastic Neural Networks with Time-Varying Discrete and Distributed Delays

Abstract

This paper investigates the problem of robust stability for a class of stochastic interval neural networks with discrete and distributed time-varying delays. The discrete delays are assumed to be varying within a given interval, while the parameter uncertainties are assumed to be bounded in some given compact sets. Based on the Ito differential formula and stochastic stability theory, delay-range-dependent criteria for stochastic interval neural networks with time-varying delays are derived to guarantee robust global asymptotic stability in mean square. In this paper, when estimating the upper bound of the derivative of Lyapunov functionals, we are concerned with better handling of terms related to the discrete and distributed delays and establishing less conservative results. These robust stability conditions are presented in terms of linear matrix inequalities and can be efficiently solved via standard numerical software. An important feature of the results proposed in this paper is that the stability conditions are dependent on the upper and lower bounds of the discrete delays. Numerical examples are given to illustrate the effectiveness of the proposed method.