Stochastic dynamic output feedback stabilization of uncertain stochastic state-delayed systems

This paper addresses the problem of stochastic dynamic output feedback (SDOF) stabilization for a class of stochastic continuous-time state-delayed systems with norm-bounded nonlinear uncertainties. The aim is to design a linear, delayless, and SDOF control for all admissible uncertainties. The designed control ensures stochastically exponentially stability in the mean square, independent of the deterministic time delay. Using the Finsler's lemma, the necessary and sufficient conditions for the existence of such a control are proposed in terms of certain linear matrix inequalities. These results are illustrated with a simple example to demonstrate the applicability of the proposed design approach.