Note on diffeomorphism extension for observer design

Abstract

An often encountered way of designing an observer is to use coordinates different from the given ones (or the ones of interest). This is done via the construction of a diffeomorphism (maybe obtained following the extension of an injective immersion) and an extended vector field on which is designed the observer. The estimated state is then obtained by employing the left inverse of the diffeomorphism (which may be difficult to obtained). A possible solution to overcome this difficulty is to use a diffeomorphism extension. A first preliminary result is given in this note