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- Lyapunov_function abstract "In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions are important to stability theory and control theory. A similar concept appears in the theory of general state space Markov Chains, usually under the name Foster-Lyapunov functions.For many classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability. Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases, the construction of Lyapunov functions is known. For instance, quadratic functions suffice for systems with one state; the solution of a particular linear matrix inequality provides Lyapunov functions for linear systems; and conservation laws can often be used to construct Lyapunov functions for physical systems.Informally, a Lyapunov function is a function that takes positive values everywhere except at the equilibrium in question, and decreases (or is non-increasing) along every trajectory of the ODE. The principal merit of Lyapunov function-based stability analysis of ODEs is that the actual solution (whether analytical or numerical) of the ODE is not required.".
- Lyapunov_function wikiPageExternalLink Lyapunov.htm.
- Lyapunov_function wikiPageExternalLink ODELF1.
- Lyapunov_function wikiPageID "352267".
- Lyapunov_function wikiPageLength "5748".
- Lyapunov_function wikiPageOutDegree "26".
- Lyapunov_function wikiPageRevisionID "632393032".
- Lyapunov_function wikiPageWikiLink Aleksandr_Lyapunov.
- Lyapunov_function wikiPageWikiLink Category:Stability_theory.
- Lyapunov_function wikiPageWikiLink Conservation_law.
- Lyapunov_function wikiPageWikiLink Conservation_law_(physics).
- Lyapunov_function wikiPageWikiLink Control-Lyapunov_function.
- Lyapunov_function wikiPageWikiLink Control_theory.
- Lyapunov_function wikiPageWikiLink Dynamical_system.
- Lyapunov_function wikiPageWikiLink Equilibrium_point.
- Lyapunov_function wikiPageWikiLink Foster-Lyapunov_functions.
- Lyapunov_function wikiPageWikiLink Fosters_theorem.
- Lyapunov_function wikiPageWikiLink José_Luis_Massera.
- Lyapunov_function wikiPageWikiLink Linear_matrix_inequality.
- Lyapunov_function wikiPageWikiLink Lyapunov_optimization.
- Lyapunov_function wikiPageWikiLink Markov_Chain.
- Lyapunov_function wikiPageWikiLink Markov_chain.
- Lyapunov_function wikiPageWikiLink Mathematician.
- Lyapunov_function wikiPageWikiLink Ordinary_differential_equation.
- Lyapunov_function wikiPageWikiLink Ordinary_differential_equations.
- Lyapunov_function wikiPageWikiLink Physical_system.
- Lyapunov_function wikiPageWikiLink Positive-definite_function.
- Lyapunov_function wikiPageWikiLink Quadratic_function.
- Lyapunov_function wikiPageWikiLink Radially_unbounded_function.
- Lyapunov_function wikiPageWikiLink Russia.
- Lyapunov_function wikiPageWikiLink Scalar_field.
- Lyapunov_function wikiPageWikiLink Scalar_function.
- Lyapunov_function wikiPageWikiLink Stability_theory.
- Lyapunov_function wikiPageWikiLinkText "Lyapunov Function".
- Lyapunov_function wikiPageWikiLinkText "Lyapunov function".
- Lyapunov_function wikiPageWikiLinkText "Lyapunov stability theorem".
- Lyapunov_function wikiPageWikiLinkText "energy function".
- Lyapunov_function wikiPageWikiLinkText "function".
- Lyapunov_function wikiPageWikiLinkText "globally asymptotically stable".
- Lyapunov_function hasPhotoCollection Lyapunov_function.
- Lyapunov_function id "4386".
- Lyapunov_function title "Lyapunov Function".
- Lyapunov_function title "Lyapunov function".
- Lyapunov_function urlname "LyapunovFunction".
- Lyapunov_function wikiPageUsesTemplate Template:Cite_book.
- Lyapunov_function wikiPageUsesTemplate Template:Main.
- Lyapunov_function wikiPageUsesTemplate Template:Mathworld.
- Lyapunov_function wikiPageUsesTemplate Template:PlanetMath_attribution.
- Lyapunov_function subject Category:Stability_theory.
- Lyapunov_function hypernym Functions.
- Lyapunov_function type Software.
- Lyapunov_function type Source.
- Lyapunov_function comment "In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions are important to stability theory and control theory.".
- Lyapunov_function label "Lyapunov function".
- Lyapunov_function sameAs دالة_ليابونوف.
- Lyapunov_function sameAs Función_de_Lyapunov.
- Lyapunov_function sameAs Fonction_de_Liapounov.
- Lyapunov_function sameAs Funzione_di_Lyapunov.
- Lyapunov_function sameAs リアプノフ関数.
- Lyapunov_function sameAs m.01zf8h.
- Lyapunov_function sameAs Функция_Ляпунова.
- Lyapunov_function sameAs ฟังก์ชันเลียปูนอฟ.
- Lyapunov_function sameAs Функція_Ляпунова.
- Lyapunov_function sameAs Q2337858.
- Lyapunov_function sameAs Q2337858.
- Lyapunov_function sameAs 李亞普諾夫函數.
- Lyapunov_function wasDerivedFrom Lyapunov_function?oldid=632393032.
- Lyapunov_function isPrimaryTopicOf Lyapunov_function.