On the Existence of a Kazantzis-Kravaris/Luenberger Observer

Vincent Andrieu (1) , Laurent Praly (2)

1 ONERA - The French Aerospace Lab [Châtillon]
2 CAS - Centre Automatique et Systèmes

We state sufficient conditions for the existence, on a given open set, of the extension, to nonlinear systems, of the Luenberger observer as it has been proposed by Kazantzis and Kravaris. We prove it is sufficient to choose the dimension of the system, giving the observer, less than or equal to 2 + twice the dimension of the state to be observed. We show that it is sufficient to know only an approximation of the solution of a PDE, needed for the implementation. We establish a link with high gain observers. Finally we extend our results to systems satisfying an unboundedness observability property.

Mots clés: nonlinear osbservers; Luenberger observers; high gain observers

Domaines: Automatique / Robotique; Optimisation et contrôle [math.OC]

Vincent Andrieu, Laurent Praly. On the Existence of a Kazantzis-Kravaris/Luenberger Observer. SIAM Journal on Control and Optimization, 2006, 45 (2), pp.432-456. ⟨10.1137/040617066⟩. ⟨hal-00362726⟩