Uniting two Control Lyapunov Functions for affine systems

Vincent Andrieu (1) , Christophe Prieur (2)

1 LAGEP - Laboratoire d'automatique et de génie des procédés
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

The problem of piecing together two Control Lyapunov Functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient condition is expressed to obtain an explicit solution. This sufficient condition is shown to be always satisfied for a linear second order controllable system. In a second part, it is shown how this uniting CLF problem can be used to solve the problem of piecing together two stabilizing control laws. Finally, this framework is applied on a numerical example to improve local performance of a globally stabilizing state feedback.

Domaines: Automatique / Robotique

Vincent Andrieu, Christophe Prieur. Uniting two Control Lyapunov Functions for affine systems. IEEE Transactions on Automatic Control, 2010, 55 (8), pp.1923-1927. ⟨hal-00552094⟩