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 in control theory |
| 93B36 | \(H^\infty\)-control |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J27 | Continuous-time Markov processes on discrete state spaces |
| 93D15 | Stabilization of systems by feedback |
Keywords:
singular Markovian jump systems; singular stochastic finite-time boundedness; singular stochastic finite-time stabilization; parametric uncertainties; linear matrix inequalities (LMIs)References:
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