Uniting two Control Lyapunov Functions for affine Systems

Vincent Andrieu (1) , Christophe Prieur (1)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

We consider the problem of piecing together two control Lyapunov functions (CLFs). The first CLF characterizes a local controllability property toward the origin, whereas the second CLF satisfies a global controllability property with respect to a compact set. We give a sufficient condition to express explicitly a solution to this uniting problem. This sufficient condition is shown to be always satisfied for a simple chain of integrator. In a second part, we show how this uniting CLF problem can be useful to solve the problem of piecing together two stabilizing control laws

Mots clés: lyapunov; stabilization; uniting controller; optimal control

Domaines: Automatique / Robotique

Vincent Andrieu, Christophe Prieur. Uniting two Control Lyapunov Functions for affine Systems. Decision and Control, 2008. CDC 2008. 47th IEEE Conference on, Dec 2008, Cancun, Mexico. pp.622 - 627, ⟨10.1109/CDC.2008.4738835⟩. ⟨hal-00457825⟩