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Delay-dependent robust \(H _{\infty }\) admissibility and stabilization for uncertain singular system with Markovian jumping parameters. (English) Zbl 1169.93420

Summary: This paper investigates the problem of delay-dependent robust \(H _{\infty }\) admissibility and stabilization for uncertain singular time delay systems with Markovian jumping parameters. The considered systems are not necessarily assumed to be regular and impulse-free. In terms of the linear matrix inequality approach, a delay-dependent stochastic admissibility criterion is given to ensure that the nominal system is regular, impulse-free and stochastically stable. Based on this criterion, the problem is solved. A numerical example is provided to demonstrate the efficiency of the proposed methods in this paper.

MSC:

93E15 Stochastic stability in control theory
60J75 Jump processes (MSC2010)
93C41 Control/observation systems with incomplete information
93B36 \(H^\infty\)-control
15A39 Linear inequalities of matrices
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