Robust reliable H∞ control for stochastic neural networks with randomly occurring delays

This paper investigates the problem of robust stabilization for a class of discrete-time stochastic neural networks with randomly occurring discrete and distributed time-varying delays. More precisely, the neuron activation functions are assumed to be more general and satisfy sector-like nonlinearities. Moreover, the effects of both variation range and probability distribution of mixed time-delays are taken into consideration in the proposed problem. The main objective of this paper is to design a state feedback reliable H∞H∞ controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop form of considered neural network is robustly asymptotically stable while satisfying a prescribed H∞H∞ performance constraint. Linear matrix inequality approach together with proper construction of Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust reliable H∞H∞ controller. The obtained results are formulated in terms of linear matrix inequalities (LMIs) which can be easily solved by using the MATLAB LMI toolbox. Finally, a numerical example with simulation results is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed results.