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Robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay. (English) Zbl 1263.93232

Summary: 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 is stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows. Furthermore, 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.

MSC:

93E15 Stochastic stability in control theory
93D09 Robust stability
93D15 Stabilization of systems by feedback
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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