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Robust \(H_{2}\) control of Markovian jump systems with uncertain switching probabilities. (English) Zbl 1167.93335

Summary: This article deals with the robust \(H_{2}\) control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust \(H_{2}\) performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust \(H_{2}\) performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory.

MSC:

93B35 Sensitivity (robustness)
60J75 Jump processes (MSC2010)
93C41 Control/observation systems with incomplete information
15A39 Linear inequalities of matrices
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