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 V
0 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.