Delay-dependent H∞ Control for Discrete-time Uncertain Recurrent Neural Networks with Intrerval Time-varying Delay

This paper deals with the problem of delay-dependent robust H∞ control for discrete-time recurrent neural networks (DRNNs) with norm-bounded parameter uncertainties and interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. For the robust stabilization problem, a state feedback controller is designed to ensure global robust stability of the closed-loop system about its equilibrium point for all admissible uncertainties, while for the robust H∞ control problem, attention is focused on the design of a state feedback controller such that 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 also required to be achieved. A linear matrix inequality approach is developed to solve these problems. It is shown that the desired state feedback controller can be constructed by solving certain LMIs. A numerical example is provided to demonstrate the effectiveness and applicability of the proposed results.