Robust Stabilization of Uncertain Stochastic Systems with Delay in Control Input

Abstract

This paper discusses the problems of robust stabilization of stochastic systems with parametric uncertainties and time delay in control input. The parametric uncertainties which appear in all system matrices are assumed to be norm bounded. The delay-dependent stabilization condition is derived by taking the relationships between terms in the Leibniz-Newton formula into account. Free-weighting matrices are employed to express these relationship, and the sufficient stabilization condition is formulated in terms of linear matrix inequality (LMI) based on the Lyapunov-Krasovskii theory, which can be solved by LMI toolbox in Matlab