Before revision: Artstein's theorem states that a dynamical system has a differentiable control-Lyapunov function if and only if there exists a regular stabilizing feedback : .Sontag
After revision: 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.