Robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay

This paper studies the problem of robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay. The state variables on the impulses are assumed dependent on the present state variables as well as delayed state variables. Based on the Razumikhin techniques and Lyapunov functions, some robust mean-square exponential stability criteria are derived in terms of linear matrix inequalities. The results show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows. Furthermore, the robust delayed-state-feedback controllers that mean-square exponentially stabilize the uncertain impulsive stochastic systems are proposed. Finally, several numerical examples are given to show the effectiveness of the results.

► A class of uncertain impulsive stochastic system with time-varying delay.
► Time delay appears both in the state variables on the impulses and control input.
► Robust mean-square exponential stability criteria are derived in terms of LMIs.
► The system will stable if impulses are suitably related to continuous flows.
► Robust delayed-state-feedback controllers are proposed.