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Robust finite-time \(H_\infty\) control for Markovian jump systems with partially known transition probabilities. (English) Zbl 1293.93773

Summary: This paper is concerned with the problem of robust finite-time \(H_\infty\) control for Markovian jump systems with partially known transition probabilities. Sufficient conditions ensuring the finite-time boundedness, \(H_\infty\) finite-time boundedness and finite-time \(H_\infty\) state feedback stabilization are, respectively, developed for the given system for the first time. A robust finite-time \(H_\infty\) state feedback controller is also designed, which guarantees the \(H_\infty\) finite-time boundedness of the closed-loop system. Seeking computational convenience, all the conditions are cast in the format of linear matrix inequalities. Finally a numerical example is provided to demonstrate the effectiveness of the main results.

MSC:

93E15 Stochastic stability in control theory
93D15 Stabilization of systems by feedback
60J75 Jump processes (MSC2010)
93B35 Sensitivity (robustness)
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