# TRIANGULAR FORMS FOR AFFINE NONLINEAR SYSTEMS WITH TWO INPUTS

Topic: All

14 avril 2008, Salle R05, au Centre Automatique et Systèmes, Fontainebleau

14h00 : Hector SILVEIRA, CAS et Université de Soa Paulo, Brésil.

This seminar treats the problem of describing affine nonlinear systems with two inputs by triangular forms, after a change of coordinates and a regular static state feedback. Based on geometric control theory, three results will be presented. The first one, establishes sufficient geometric conditions for a system to be described by a triangular form around every point of some dense open set. Furthermore, the resulting triangular form implies that the system is flat around every point of an open subset. It will also be shown that if a system is described by a triangular form around a given point, then these same geometric conditions are necessarily satisfied around the point. Finally, the last result presents sufficient conditions for a flat system with two inputs and five or less states to be described by a triangular form.

14h00 : Hector SILVEIRA, CAS et Université de Soa Paulo, Brésil.

This seminar treats the problem of describing affine nonlinear systems with two inputs by triangular forms, after a change of coordinates and a regular static state feedback. Based on geometric control theory, three results will be presented. The first one, establishes sufficient geometric conditions for a system to be described by a triangular form around every point of some dense open set. Furthermore, the resulting triangular form implies that the system is flat around every point of an open subset. It will also be shown that if a system is described by a triangular form around a given point, then these same geometric conditions are necessarily satisfied around the point. Finally, the last result presents sufficient conditions for a flat system with two inputs and five or less states to be described by a triangular form.