A unified H_inf adaptive observer synthesis method for a class of systems with both lipschitz and monotone nonlinearities

Ali Zemouche (1, 2) , Mohamed Boutayeb (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

This paper investigates the problem of H_inf adaptive observer design for a class of nonlinear dynamical systems. The main contribution consists in providing a unified synthesis method for systems with both Lipschitz and monotone nonlinearities (not necessarily Lipschitz). Thanks to the innovation terms into the nonlinear functions [18] and to the differential mean value theorem [5], the stability analysis leads to the solvability of a Linear Matrix Inequality (LMI) with several degrees of freedom. For simplicity, we start by presenting the result in an H_inf adaptive-free context. Furthermore, we propose an H_inf adaptive estimator that extends easily the obtained results to systems with unknown parameters in the presence of disturbances. We show, in particular, that the matching condition in terms of an equality constraint required in several works is not necessary and therefore allows reducing the conservatism of the existing conditions. Performances of the proposed approach are shown through a numerical example with a polynomial nonlinearity.

Mots clés: State observers; nonlinear systems; LMI approach; the Differential Mean Value Theorem (DMVT); $\mathcal{H}_{\infty}$ adaptive estimator

Domaines: Automatique / Robotique

Ali Zemouche, Mohamed Boutayeb. A unified H_inf adaptive observer synthesis method for a class of systems with both lipschitz and monotone nonlinearities. Systems and Control Letters, 2009, 58 (4), pp.282-288. ⟨10.1016/j.sysconle.2008.11.007⟩. ⟨hal-00353208⟩