Artstein's theorem
id:
artstein-s-theorem-195-2957706
title:
Artstein's theorem
text:
Artstein's theorem states that a nonlinear dynamical system in the control-affine form x ˙ = f ( x ) + ∑ i = 1 m g i ( x ) u i 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.
brand slug:
wiki
category slug:
encyclopedia
description:
Theorem in control theory
original url:
https://en.wikipedia.org/wiki/Artstein%27s_theorem
date created:
date modified:
2023-04-17T07:33:47Z
main entity:
{"identifier":"Q4801563","url":"https://www.wikidata.org/entity/Q4801563"}
image:
fields total:
13
integrity:
14