Robust observer design for Itô stochastic time-delay systems via sliding mode control

This paper deals with the output feedback sliding mode control for Itô stochastic time-delay systems. The system states are unmeasured, and the uncertainties are unmatched. A sliding mode control scheme is proposed based on the state estimates. By utilizing a novel switching function, the derivative of the switching function is ensured to be finite variation. It is shown that the sliding mode in the estimation space can be attained in finite time. The sufficient condition for the asymptotic stability (in probability) of the overall closed-loop stochastic system is derived. Finally, a simulation example is shown to illustrate the proposed method.