A class of perturbations which do not affect local controllability (Q791866)

Given a finite family of analytic vector fields F in a neighborhood of the origin of \({\mathbb{R}}^ n\), we are interested in the following property: the origin is an interior point of the reachable set from the origin itself at each positive instant. We describe a class of small perturbations, acting on the terms of the Taylor expansion of the vector fields of F from some order on, which do not destroy the property above.