Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems

Free access article

Issue		ESAIM: COCV Volume 5, 2000


Page(s)		293 - 311
DOI		10.1051/cocv:2000112

DOI: 10.1051/cocv:2000112

ESAIM: COCV, June 2000, Vol. 5, 293-311

Control Lyapunov functions for homogeneous "Jurdjevic-Quinn'' systems

Ludovic Faubourg
INRIA, BP. 93, 06902 Sophia Antipolis, France; (Ludovic.Faubourg@sophia.inria.fr)

Jean-baptiste Pomet
INRIA, BP. 93, 06902 Sophia Antipolis, France; (Jean-Baptiste.Pomet@sophia.inria.fr)

Received July 1, 1999. Revised May 4, 2000

Abstract: This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called "Jurdjevic-Quinn conditions''. For these systems a positive definite function V₀ is known that can only be made non increasing by feedback. We describe how a control Lyapunov function can be obtained via a deformation of this "weak'' Lyapunov function. Some examples are presented, and the linear quadratic situation is treated as an illustration.

Résumé: Cet article présente une méthode permettant de construire explicitement des fonctions de Lyapunov contrôlées pour des systèmes affines et homogènes vérifiant les conditions dites "de Jurdjevic-Quinn''. Pour de tels systèmes, on connaît une fonction définie positive V₀ et une loi de commande qui fait seulement décroître V₀, avec une dérivée qui peut s'annuler en certains points. Nous montrons comment il est possible d'obtenir une fonction de Lyapunov contrôlée via une déformation de cette fonction de Lyapunov "au sens large''. Quelques exemples sont présentés, et le cas linéaire quadratique est traité comme illustration.

Keywords and phrases: Feedback stabilization, control Lyapunov function, Lyapunov design.

AMS Subject Classification: 93D15, 93D30, 34D20

Article with figures

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