Control lyapunov functions for homogeneous “jurdjevic-quinn” systems

Abstract

This paper presents a method to design explicit control Lyapunov functions for afine 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. © 2000 EDP Sciences, SMAI.