## 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)