# Robust observer-based $H_{\infty}$ stabilization for a class of switched discrete-time linear systems with parameter uncertainties

2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
Abstract : This paper presents a robust observer-based $H_\infty$ controller design method via LMIs for a class of switched discrete-time linear systems with $l_2$-bounded disturbances and parameter uncertainties. The main contribution of this paper consists in a new and judicious use of the slack variables coming from Finsler's lemma. We show analytically how the proposed slack variables allow to eliminate some bilinear matrix coupling. The validity and effectiveness of the proposed design methodology are shown through two numerical examples.
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Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-01674803
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### Citation

Hamza Bibi, Ali Zemouche, Abdel Aitouche, Khadidja Chaib Draa, Fazia Bedouhene. Robust observer-based $H_{\infty}$ stabilization for a class of switched discrete-time linear systems with parameter uncertainties. 56th IEEE Conference on Decision and Control, CDC 2017, Dec 2017, Melbourne, Australia. ⟨10.1109/cdc.2017.8264442⟩. ⟨hal-01674803⟩

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