Robust variance control for a class of nonlinear discrete systems with uncertainties and time-delay

This paper deals with the problem of robust variance control design for a class of uncertain nonlinear discrete time-delay systems. The system under consideration involves state time delay, nonlinear, parameter uncertainties and white noise disturbances. The purpose of this problem is to design a static state feedback controller such that not only the resulting closed-loop system is asymptotically stable, but also the steady-state variance of each state is not more than the individual pre-specified value simultaneously. Using the linear matrix inequality approach in this paper, the existence conditions of such controllers are derived. Furthermore, a numerical example is given to illustrate the effectiveness of the proposed approach.