On the existence of local smooth repulsive stabilizing feedbacks in dimension three

Ludovic Rifford (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

Given an affine control system in $\R^3$ subject to the Hörmander's condition at the origin, we prove the existence of a local smooth repulsive stabilizing feedback at the origin. Our construction is based on the classical homogeneization procedure, on the existence of a semiconcave control-Lyapunov function, and on the classification of singularities of semiconcave functions in dimension two.

Domaines: Géométrie différentielle [math.DG]; Optimisation et contrôle [math.OC]

Ludovic Rifford. On the existence of local smooth repulsive stabilizing feedbacks in dimension three. Journal of Differential Equations, 2005, 226 (2), pp.429-500. ⟨hal-00769046⟩