Lyapunov theory is a collection of results regarding stability of
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Lyapunov exponent — In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories in phase space with… … 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
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 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 — 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's central limit theorem — In probability theory, Lyapunov s central limit theorem is one of the variants of the central limit theorem. Unlike the classical central limit theorem, which requires that the random variables in question be both independent and identically… … Wikipedia
Aleksandr Lyapunov — Infobox Scientist name = Aleksandr Mikhailovich Lyapunov caption = birth date = birth date|1857|6|6 birth place = Yaroslavl, Imperial Russia death date = death date and age|1918|11|3|1857|6|6 death place = residence = Russia citizenship =… … Wikipedia
Chaos theory — This article is about chaos theory in Mathematics. For other uses of Chaos theory, see Chaos Theory (disambiguation). For other uses of Chaos, see Chaos (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 … Wikipedia
Control theory — For control theory in psychology and sociology, see control theory (sociology) and Perceptual Control Theory. The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is… … Wikipedia
Control-Lyapunov function — In control theory, a control Lyapunov function V(x,u) [1]is a generalization of the notion of Lyapunov function V(x) used in stability analysis. The ordinary Lyapunov function is used to test whether a dynamical system is stable (more… … Wikipedia
