$H_\infty$ circle criterion observer design for Lipschitz nonlinear systems with enhanced LMI conditions

Ali Zemouche (1) , Rajesh Rajamani (2) , Boulaïd Boulkroune (3) , Hugues Rafaralahy (1) , Michel Zasadzinski (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 ECE - Department of Electrical and Computer Engineering [Minneapolis]
3 STF - Systèmes Tolérants aux Fautes

This note deals with observer design for Lipschitz nonlinear systems via LMI. A new LMI condition is proposed to solve the problem of mathcal{H}_{infty} circle criterion observer design. This enhanced LMI is less conservative than those proposed in the literature for the same class of systems by using the same methodology. Indeed, thanks to a new and judicious use of the Young's relation, additional degree of freedoms are included in the LMI, contrarily to some recent results, which turn to be particular cases of what we proposed in this paper. This additional decision variables allow to improve the feasibility of the proposed LMI. A numerical example is given to show the effectiveness of the proposed methodology.

Mots clés: Observers for nonlinear systems; LMIs; Lyapunov methods

Domaines: Automatique / Robotique

Ali Zemouche, Rajesh Rajamani, Boulaïd Boulkroune, Hugues Rafaralahy, Michel Zasadzinski. $H_\infty$ circle criterion observer design for Lipschitz nonlinear systems with enhanced LMI conditions. American Control Conference, ACC'2016, Jul 2016, Boston, United States. ⟨hal-01293986⟩