$\mathcal{H}_{\infty}$ observer-based stabilization of switched discrete-time linear systems

Hamza Bibi (1) , Fazia Bedouhene (1) , Ali Zemouche (2, 3) , Abdel Aitouche (4)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées [Tizi-Ouzou]
2 CRAN - Centre de Recherche en Automatique de Nancy
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

This paper deals with observer-based mathcal{H}_infty controller design method via LMIs for a class of switched discrete-time linear systems with l_2-bounded disturbances. The main contribution of this note consists in a new and judicious use of the slack variables coming from Finsler's lemma. We clarify analytically how the proposed slack variables allows to eliminate some bilinear matrix coupling. The validity and effectiveness of the proposed design methodology are shown through a numerical example.

Mots clés: Switching Lyapunov Function (SLF); Finsler's lemma; Observer-based control; Linear matrix in- equalities (LMIs)

Domaines: Automatique

Hamza Bibi, Fazia Bedouhene, Ali Zemouche, Abdel Aitouche. $\mathcal{H}_{\infty}$ observer-based stabilization of switched discrete-time linear systems. 6th International Conference on Systems and Control, ICSC 2017, May 2017, Batna, Algeria. ⟨10.1109/icosc.2017.7958735⟩. ⟨hal-01567356⟩