Design of a robust controller on stabilization of stochastic neural networks with time varying delays

Abstract

This paper is concerned with the problem of robust stabilization and H∞ control for a class of uncertain stochastic neural networks with time-varying delays and time-varying norm-bounded parameter uncertainties. The delay is of a time-varying nature, and the activation functions are assumed to be neither differentiable nor strictly monotonic. Moreover, the description of the activation functions is more general than the commonly used Lipschitz conditions. By using the Lyapunov function approach together with the linear matrix inequality (LMI) technique, for the robust stabilization we propose a state feedback controller to ensure that the closed loop system is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. For the robust H∞ control problem, a state feedback controller is designed such that in addition to the requirement of robust stability, a prescribed H∞ performance level is to be satisfied. The results obtained are formulated in terms of LMIs which can be easily checked by the MATLAB LMI control toolbox. Numerical examples are presented to illustrate the effectiveness of the obtained method and the improvement over some existing results.