Robust stabilization of hybrid uncertain stochastic systems with time-varying delay by discrete-time feedback control

Abstract This paper is concerned with the robust stabilization problem for a class of continuous-time hybrid uncertain stochastic systems with time-varying delay. Our attention is focused on the design of a feedback controller based on discrete-time state observations such that, for all admissible uncertainties, the closed-loop system is robustly exponentially stable in the mean square, independent of the time delay. By employing the Razumikhin technique, sufficient conditions are firstly established to guarantee the existence of the desired robust controller; they are given in terms of linear matrix inequalities (LMIs). It should be pointed out that in this paper the time-varying delay is just required to be a bounded function rather than a bounded differentiable one as in most existing results. The developed theory is illustrated by a numerical example.