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Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems

Published online by Cambridge University Press:  15 August 2002

ludovic faubourg  and
jean-baptiste pomet
ludovic faubourg
Affiliation:
INRIA, BP. 93, 06902 Sophia Antipolis, France; Ludovic.Faubourg@sophia.inria.fr.
jean-baptiste pomet
Affiliation:
INRIA, BP. 93, 06902 Sophia Antipolis, France; Jean-Baptiste.Pomet@sophia.inria.fr.
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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.

Keywords

Feedback stabilizationcontrol Lyapunov functionLyapunov design.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 293 - 311
Copyright
© EDP Sciences, SMAI, 2000

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