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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 wikiPageRevisionID "605288118".
- 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 subject Category:Stability_theory.
- 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 "Fonction de Liapounov".
- Lyapunov_function label "Función de Lyapunov".
- Lyapunov_function label "Funzione di Lyapunov".
- Lyapunov_function label "Lyapunov function".
- Lyapunov_function label "Функция Ляпунова".
- Lyapunov_function label "دالة ليابونوف".
- Lyapunov_function label "リアプノフ関数".
- Lyapunov_function label "李亞普諾夫函數".
- 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 Q2337858.
- Lyapunov_function sameAs Q2337858.
- Lyapunov_function wasDerivedFrom Lyapunov_function?oldid=605288118.
- Lyapunov_function isPrimaryTopicOf Lyapunov_function.