ON THE EQUIVALENCE BETWEEN DIFFERENTIAL FLATNESS AND DYNAMIC FEEDBACK LINEARIZABILITY

The equivalence between dynamic feedback linearizability and flatness was listed in (Fliess et al., 1999a) as one of the open problems in the field of Nonlinear System Theory. More precisely it is shown in (Fliess et al., 1999b) that differential flatness is equivalent to endogeneous dynamic feedback linearizability, whereas the original definition of dynamic feedback linearizability involves more general dynamic feedbacks called regular. We prove in this paper the equivalence between the two definitions for general meromorphic nonlinear systems as a consequence of the necessary and sufficient conditions obtained in (Lévine, 2004; Lévine, 2006).