Robust H∞ control for uncertain discrete-time stochastic neural networks with time-varying delays

Abstract

In the last few years, the H∞ control problem has attracted much attention because of its both practical and theoretical importance. This study presents a robust H∞ control design approach for a class of uncertain discrete-time stochastic neural networks with time-varying delays. The neural network under consideration is subject to time-varying and norm bounded parameter uncertainties. For the robust stabilisation problem, a state feedback controller is designed to ensure global robust stability of the closed-loop form of neural network about its equilibrium point for all admissible uncertainties. In addition, to the requirement of the global robust stability, a prescribed H∞ performance level for all delays to satisfy both the lower bound and upper bound of the interval time-varying delay is required to be obtained. Through construction of a new Lyapunov–Krasovskii functional, a robust H∞ control scheme is presented in terms of linear matrix inequalities (LMIs). The controller gains can be derived by solving a set of LMIs. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the developed theoretical results.