Delay-Dependent Robust Stability of Uncertain Stochastic Nonlinear Time-Varying Systems with Time-Delays

Abstract

This paper deals with the problem of stochastic robust asymptotically stability for a class of uncertain stochastic nonlinear time-varying systems with time-delays. The parametric uncertainties are assumed to be time-varying and norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim of this paper is to design a memory less state feedback control law such that the closed-loop system is stochastically asymptotical stable in the mean square for all admissible parameter uncertainties. A new sufficient condition for the existence of such controllers is presented based on the linear matrix inequality (LMI) approach. Numerical example is given to illustrate the effectiveness of the developed method.