Delay-dependent robust H<inf>∞</inf> control for nonlinear uncertain stochastic systems with time delay

Abstract

In this paper, the problem of robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control for a class of nonlinear uncertain stochastic systems with time delay both in state equation and output equation is discussed. Uncertainties of nonlinear perturbation are assumed to be norm bounded. Based on estimating the upper bound of the stochastic differential of Lyapunov function and constructing some LMIs, we give a memoryless robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller design example which ensures the closed-loop system which is robustly stochastically stable and satisfies the robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance index for all admissible uncertainties. Sufficient conditions in terms of linear matrix inequalities which have a feasible solution are presented. Finally, a numerical example is given to show the effectiveness and feasibility of the proposed method.