Artstein's theorem

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}.

[1] 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.

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