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- Lyapunov_stability abstract "Various types of stability may be discussed for the solutions of differential equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Lyapunov. In simple terms, if all solutions of the dynamical system that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is asymptotically stable. The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs.".
- Lyapunov_stability wikiPageExternalLink non-linear-controls-lab.
- Lyapunov_stability wikiPageID "363360".
- Lyapunov_stability wikiPageRevisionID "604435740".
- Lyapunov_stability hasPhotoCollection Lyapunov_stability.
- Lyapunov_stability id "4679".
- Lyapunov_stability title "asymptotically stable".
- Lyapunov_stability subject Category:Dynamical_systems.
- Lyapunov_stability subject Category:Stability_theory.
- Lyapunov_stability type Abstraction100002137.
- Lyapunov_stability type Attribute100024264.
- Lyapunov_stability type DynamicalSystem106246361.
- Lyapunov_stability type DynamicalSystems.
- Lyapunov_stability type PhaseSpace100029114.
- Lyapunov_stability type Space100028651.
- Lyapunov_stability comment "Various types of stability may be discussed for the solutions of differential equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Lyapunov. In simple terms, if all solutions of the dynamical system that start out near an equilibrium point stay near forever, then is Lyapunov stable.".
- Lyapunov_stability label "Estabilidad de Lyapunov".
- Lyapunov_stability label "Lyapunov stability".
- Lyapunov_stability label "Metody Lapunowa".
- Lyapunov_stability label "Stabilità interna".
- Lyapunov_stability label "Stabilité de Lyapunov".
- Lyapunov_stability label "Устойчивость (динамические системы)".
- Lyapunov_stability label "リアプノフ安定".
- Lyapunov_stability label "李雅普诺夫稳定性".
- Lyapunov_stability sameAs Estabilidad_de_Lyapunov.
- Lyapunov_stability sameAs Stabilité_de_Lyapunov.
- Lyapunov_stability sameAs Stabilità_interna.
- Lyapunov_stability sameAs リアプノフ安定.
- Lyapunov_stability sameAs 랴푸노프_안정성.
- Lyapunov_stability sameAs Metody_Lapunowa.
- Lyapunov_stability sameAs m.01_ppq.
- Lyapunov_stability sameAs Q1341651.
- Lyapunov_stability sameAs Q1341651.
- Lyapunov_stability sameAs Lyapunov_stability.
- Lyapunov_stability wasDerivedFrom Lyapunov_stability?oldid=604435740.
- Lyapunov_stability isPrimaryTopicOf Lyapunov_stability.