Stratified semiconcave control-Lyapunov functions and the stabilization problem

Ludovic Rifford (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

Given a globally asymptotically controllable control system, we construct a control-Lyapunov function which is stratified semiconcave;that is, roughly speaking whose singular set has a Whitney stratification. Then we deduce the existence of smooth feedbacks which make the closed-loop system almost globally asymptotically stable.

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Ludovic Rifford. Stratified semiconcave control-Lyapunov functions and the stabilization problem. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2005, 22 (3), pp.343-384. ⟨hal-00769045⟩