Robust ?? control of descriptor discrete-time Markovian jump systems

Lam, James, Shu, Zhan, Xu, Shengyuan and Boukas, E.K. (2007) Robust ?? control of descriptor discrete-time Markovian jump systems. International Journal of Control, 80 (3), 374-385. (doi:10.1080/00207170600999322).

Record type: Article

Abstract

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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