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Robust finite-time stabilization of uncertain singular Markovian jump systems. (English) Zbl 1252.93130
Summary: This paper focuses on the problem of robust finite-time stabilization for one family of uncertain singular Markovian jump systems. Firstly, the definitions of singular stochastic finite-time boundedness and singular stochastic ${H}_{\infty }$ finite-time boundedness are presented. Secondly, sufficient conditions on singular stochastic finite-time boundedness are obtained for the class 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 family of singular stochastic systems. Sufficient criteria are provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic finite-time boundedness and singular stochastic ${H}_{\infty }$ finite-time boundedness, which can be reduced to a feasibility problem in the form of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to illustrate the validity of the proposed methodology.
##### MSC:
 93E15 Stochastic stability 93B36 ${H}^{\infty }$-control 60H10 Stochastic ordinary differential equations 60J27 Continuous-time Markov processes on discrete state spaces 93D15 Stabilization of systems by feedback