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Robust finite-time ${H}_{\infty }$ control of singular stochastic systems via static output feedback. (English) Zbl 1238.93121
Summary: This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic ${H}_{\infty }$ finite-time boundedness for the class of singular stochastic systems. An algorithm for static output feedback controller is designed to guarantee that the underlying closed-loop singular stochastic system is singular stochastic ${H}_{\infty }$ finite-time bounded in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology.
##### MSC:
 93E15 Stochastic stability 93D15 Stabilization of systems by feedback 93B36 ${H}^{\infty }$-control 93C15 Control systems governed by ODE