Stabilization of hybrid stochastic differential delay equations by feedback control based on discrete-time state observation

For an unstable hybrid stochastic differential delay equation, this paper designs a feedback control based on discrete-time state observation to make the controlled system become almost sure exponential stability. In order to reveal the relationship between the two features contained in the system, namely, the dependence of duration between two consecutive observations on time-delay, the method of Lyapunov functional and auxiliary system are combined in this paper. It is shown that the underlying system possesses almost sure exponential stability for sufficiently small time-interval between two consecutive observations. Finally, an illustrative example is given to show the effectiveness of the proposed control strategy.