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Robust stochastic stabilization and \(H_{\infty}\) control of uncertain neutral stochastic time-delay systems. (English) Zbl 1127.93053
Summary: This paper investigates the problems of robust stochastic stabilization and robust \(H_{\infty}\) control for uncertain neutral stochastic time-delay systems with time-varying norm-bounded parameter uncertainties appearing in both the state and input matrices. The time delay is assumed to be unknown. Sufficient conditions for the existence of state feedback controllers are proposed, which ensure mean-square asymptotic stability of the resulting closed-loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. A linear matrix inequality approach is employed to design the desired state feedback controllers. Furthermore, in the case when time delays appear in both the state and control input, results on the robust stochastic stabilization and robust \(H_{\infty}\) control are also presented. An illustrative example is provided to show the potential of the proposed techniques.

MSC:
93D15 Stabilization of systems by feedback
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
93E15 Stochastic stability in control theory
93B36 \(H^\infty\)-control
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