About: Artstein's theorem

An Entity of Type: WikicatTheoremsInDynamicalSystems, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

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 proceeds by a nonconstructive argument. In 1989 Eduardo D. Sontag provided a constructive version of this theorem explicitly exhibiting the feedback.

Property Value
dbo:abstract
  • 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 proceeds by a nonconstructive argument. In 1989 Eduardo D. Sontag provided a constructive version of this theorem explicitly exhibiting the feedback. (en)
  • Artstein定理指出一动态系統有可微分的控制李亞普諾夫函數的充份必要條件是存在穩定回授（stabilizing feedback）：. 也就是對於以下的系統 存在控制律 可以使系統穩定。 (zh)
dbo:wikiPageID
  • 14559354 (xsd:integer)
dbo:wikiPageLength
  • 1786 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1101013112 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdf:type
rdfs:comment
  • 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 proceeds by a nonconstructive argument. In 1989 Eduardo D. Sontag provided a constructive version of this theorem explicitly exhibiting the feedback. (en)
  • Artstein定理指出一动态系統有可微分的控制李亞普諾夫函數的充份必要條件是存在穩定回授（stabilizing feedback）：. 也就是對於以下的系統 存在控制律 可以使系統穩定。 (zh)
rdfs:label
  • Artstein's theorem (en)
  • Artstein定理 (zh)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License