| 释义 |
Lyapunov stability An equilibrium of a dynamical system is Lyapunov stable if any suitably small perturbation from the equilibrium results in the system staying near the equilibrium forever. More precisely, given a metric d on the phase space, an equilibrium e is Lyapunov stable if for all ε > 0 there exists δ > 0 so that if d(x(0),e) < δ, then d(x(t),e) < ε for all t, where x(t) denotes the evolution of the system following the perturbation. Further, the equilibrium is said to be asymptotically stable if x(t) → e as t→∞ if d(x(0),e) < δ.
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