Lam, James, Shu, Zhan, Xu, Shengyuan and Boukas, E.K.
Robust ?? control of descriptor discrete-time
Markovian jump systems
International Journal of Control, 80, (3), . (doi:10.1080/00207170600999322).
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This paper considers the stochastic stability and the robust control of descriptor discrete-time systems with Markovian jumping parameters. In terms of linear matrix inequalities, a necessary and sufficient condition is proposed, which ensures a discrete-time descriptor Markovian jump system to be regular, causal and stochastically stable. A robust admissibility condition and a robust bounded real lemma are also developed. Based on these, a sufficient condition on the existence of a state-feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique. A robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.
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