International Federation of Automatic Control
3rd IFAC SYMPOSIUM on SYSTEM, STRUCTURE and CONTROL

Foz do Iguassu, Brazil October 17th - 19th, 2007

Thursday Morning

Session TM2: Non-linear systems II


Chair: Hebertt Sira-Ramírez - Mexico
Co-chair: Jean Lévine - France
Room: Montevideo
2007-10-18
From 10:00 to 12:00
On the Equivalence Between Differential Flatness and Dynamic Feedback Linearization
Jean Lévine
Contact: Jean Lévine - France
10:20-10:40
Abstract:
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)) and (Lévine (2006)). Copyright © 2007 IFAC.