asymptotically stable

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• Stable curve — In algebraic geometry, a stable curve is an algebraic curve that is asymptotically stable in the sense of geometric invariant theory. This is equivalent to the condition that it is a complete connected curve whose only singularities are ordinary… …   Wikipedia

• Evolutionarily stable state — A population is said to be in an evolutionarily stable state if its genetic composition is restored by selection after a disturbance, provided the disturbance is not too large. Such a population can be genetically monomorphic or polymorphic.… …   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

• Asymptotic stability — See also Lyapunov stability for an alternate definition used in dynamical systems. In control theory, a continuous linear time invariant system is asymptotically stable if and only if the system has eigenvalues only with strictly negative real… …   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

• 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 — /steuh bil i tee/, n., pl. stabilities. 1. the state or quality of being stable. 2. firmness in position. 3. continuance without change; permanence. 4. Chem. resistance or the degree of resistance to chemical change or disintegration. 5.… …   Universalium

• Marginal stability — In the theory of dynamical systems, and control theory, a continuous linear time invariant system is marginally stable if and only if the real part of every eigenvalue (or pole) in the system s transfer function is non positive, and all… …   Wikipedia

• Krasovskii–LaSalle principle — The Krasovskii–LaSalle principle is a criterion for the asymptotic stability of a (possibly nonlinear) dynamical system. The global Krasovskii–LaSalle principle Given a representation of the system: dot{mathbf{x = f left(mathbf x ight) where… …   Wikipedia

• Poincaré map — In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional… …   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