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.