On the Existence of a Kazantzis-Kravaris/Luenberger Observer

TL;DR

This paper provides sufficient conditions for extending the Luenberger observer to nonlinear systems, including bounds on system dimension, approximation requirements, and connections to high gain observers.

Contribution

It introduces new criteria for the existence of Kazantzis-Kravaris/Luenberger observers for nonlinear systems, including dimension bounds and approximation methods.

Findings

Observer existence under specified conditions

Dimension bound of 2 + twice the state dimension

Extension to systems with unboundedness observability

Abstract

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.