A matrix Lie group of Carnot type for filiform sub-Riemannian structures and its application to control systems in chained form

Claudio Altafini

Proceedings of the Summer school on Differential Geometry Coimbra, Portugal, September 1999

A Carnot group G is a simply connected graded nilpotent Lie group endowed a left-invariant distribution generating the Lie algebra of G. Here we show that the quotient manifold of a filiform Carnot group by the subgroup generated by its characteristic line field is projectively abelian. The result is used to show how a class of bilinear control systems have an intrinsic linear behavior.

postscript file (g-zipped)