# Robust $H_\infty$ observer-based stabilization of linear discrete-time systems with parameter uncertainties

3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : This paper addresses the problem of observer-based stabilization of discrete-time linear systems in presence of parameter uncertainties and $ell_2$-bounded disturbances. We propose a new variant of the classical two-steps LMI approach. In the first step, we use a slack variable technique to solve the optimization problem resulting from the stabilization problem by a static state feedback. In the second step, a part of the slack variable obtained is incorporated in the $H_\infty$ observer-based stabilization problem, to calculate simultaneously the Lyapunov matrix and the observer-based controller gains. A numerical evaluation is presented to show the superiority of the proposed Modified Two-Steps Method (MTSM) from LMI feasibility point of view.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01736812
Contributor : Abdel Aitouche <>
Submitted on : Sunday, March 18, 2018 - 4:40:08 PM
Last modification on : Friday, April 12, 2019 - 1:01:12 PM

### Citation

Cherifa Bennani, Fazia Bedouhene, Ali Zemouche, Hamza Bibi, Khadidja Chaib Draa, et al.. Robust $H_\infty$ observer-based stabilization of linear discrete-time systems with parameter uncertainties. IEEE American Control Conference (ACC 2018), Jun 2018, Milwaukee, WI, United States. ⟨10.23919/ACC.2018.8431745⟩. ⟨hal-01736812⟩

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