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Lyapunov stability

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  • Lyapunov stability — In mathematics, the notion of Lyapunov stability occurs in the study of dynamical systems. In simple terms, if all solutions of the dynamical system that start out near an equilibrium point x e stay near x e forever, then x e is Lyapunov stable.… …   Wikipedia

  • Lyapunov stability — stabilumas pagal Liapunovą statusas T sritis automatika atitikmenys: angl. Lyapunov stability vok. Ljapunov Stabilität, f rus. устойчивость по Ляпунову, f pranc. stabilité au sens de Lyapunov, f …   Automatikos terminų žodynas

  • Lyapunov — may refer to:* Prokopy Lyapunov (? 1611), Russian statesman. * Zakhary Lyapunov (? after 1612), Russian statesman, Prokopy Lyapunov s brother. * Mikhail Lyapunov (1820 1868), Russian astronomer * Aleksandr Lyapunov (1857–1918), Russian… …   Wikipedia

  • Lyapunov theory — is a collection of results regarding stability of dynamical systems, named after a Russian mathematician Aleksandr Mikhailovich Lyapunov. The primary result of the theory is the concept of Lyapunov stability …   Wikipedia

  • Stability — can refer to: *Aircraft flight Stability (aircraft) *In atmospheric fluid dynamics, atmospheric stability, a measure of the turbulence in the ambient atmosphere *BIBO stability (Bounded Input, Bounded Output stability), in signal processing and… …   Wikipedia

  • Lyapunov function — In mathematics, Lyapunov functions are functions which can be used to prove the stability of a certain fixed point in a dynamical system or autonomous differential equation. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov,… …   Wikipedia

  • Stability theory — In mathematics, stability theory deals with the stability of solutions (or sets of solutions) for differential equations and dynamical systems. Definition Let (R, X, Φ) be a real dynamical system with R the real numbers, X a locally compact… …   Wikipedia

  • LYAPUNOV — RUSSIA (see also List of Individuals) 25.5.1857 Jaroslav/RU 3.11.1918 Odessa/RU Aleksandr Mikhailovich Lyapunov graduated in physics and mathematics from the Saint Petersburg University in 1880. Based on a notable work on rotational flow, he was… …   Hydraulicians in Europe 1800-2000

  • Lyapunov equation — In control theory, the discrete Lyapunov equation is of the form:A X A^H X + Q = 0where Q is a hermitian matrix. The continuous Lyapunov equation is of form:AX + XA^H + Q = 0.The Lyapunov equation occurs in many branches of control theory, such… …   Wikipedia

  • Lyapunov fractal — Standard Lyapunov logistic fractal with iteration sequence AB, in the region [2, 4] × [2, 4] …   Wikipedia

  • Stability of the Solar System — The stability of the Solar System is a subject of much inquiry in astronomy. The Solar System is chaotic,cite journal title=Large scale chaos in the solar system author=J. Laskar journal=Astronomy and Astrophysics volume=287 pages=L9 ndash;L12… …   Wikipedia

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