Artstein's theorem states that a nonlinear dynamical system in the control-affine form has a differentiable control-Lyapunov function if and only if it admits a regular stabilizing feedback u(x), that is a locally Lipschitz function on Rn\{0}. The original 1983 proof by Zvi Artstein proceeds by a nonconstructive argument. In 1989 Eduardo D. Sontag provided a constructive version of this theorem explicitly exhibiting the feedback. See also Analysis and control of nonlinear systems Control-Lyapunov function References Control theory Theorems in dynamical systems