On the Existence of a Kazantzis-Kravaris/Luenberger Observer

Details On the Existence of a Kazantzis-Kravaris/Luenberger Observer On the Existence of a Kazantzis-Kravaris/Luenberger Observer

2009-03-02

arxiv.org/abs/0903.0297v1

SIAM Journal on Control and Optimization 45, 2 (2006) 432-456

Mathematics

Optimization and Control

Scientific paper

10.1137/040617066

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.

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