Circle criterion-based $\mathcal{H}_{\infty}$ observer design for Lipschitz and monotonic nonlinear systems - Enhanced LMI conditions and constructive discussions

Ali Zemouche (1, 2) , Rajesh Rajamani (3) , Gridsada Phanomchoeng (4) , Boulaïd Boulkroune (5) , Hugues Rafaralahy (1) , Michel Zasadzinski (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 ECE - Department of Electrical and Computer Engineering [Minneapolis]
4 Chulalongkorn University [Bangkok]
5 ULB - Université libre de Bruxelles

A new LMI design technique is developed to address the problem of circle criterion-based $\mathcal{H}_{\infty}$ observer design for nonlinear systems. The developed technique applies to both locally Lipschitz as well as monotonic nonlinear systems, and allows for nonlinear functions in both the process dynamics and output equations. The LMI design condition obtained is less conservative than all previous results proposed in the literature for these classes of nonlinear systems. By judicious use of a modified Young’s relation, additional degrees of freedom are included in the observer design. These additional decision variables enable improvements in the feasibility of the obtained LMI. Several recent results in the literature are shown to be particular cases of the more general observer design methodology developed in this paper. Illustrative examples are given to show the effectiveness of the proposed methodology. The application of the method to slip angle estimation in automotive applications is discussed and experimental results are presented.

Mots clés: slip angle estimation; $\mathcal{H}_{\infty}$ synthesis; Observers design; Lipschitz systems; LMI approach; Lipschitz systems; LMI approach; H ∞ synthesis; slip angle estimation

Domaines: Automatique; Sciences de l'ingénieur [physics]

Ali Zemouche, Rajesh Rajamani, Gridsada Phanomchoeng, Boulaïd Boulkroune, Hugues Rafaralahy, et al.. Circle criterion-based $\mathcal{H}_{\infty}$ observer design for Lipschitz and monotonic nonlinear systems - Enhanced LMI conditions and constructive discussions. Automatica, 2017, 85, pp.412-425. ⟨10.1016/j.automatica.2017.07.067⟩. ⟨hal-01567360⟩