Geometrical conditions for observer error linearization with a diffeomorphism on the outputs

This paper gives the sufficient and necessary conditions which guarantee the existence of a diffeomorphism which transforms the dynamic of a multi outputs nonlinear system without input into a linear dynamic up to a vector field which depends only on the outputs. The same diffeomorphism yields a diffeomorphism on the outputs. In this case we can design an observer which linearizes the error of the dynamical system under consideration.