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