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单词 LyapunovStable
释义

Lyapunov stable


A fixed pointMathworldPlanetmath x* is Lyapunov stablePlanetmathPlanetmath if trajectories of nearby points x remain close for future time. More formally the fixed point x* is Lyapunov stable, if for any ϵ>0, there is a δ>0 such that for all t0 and for all xx* it is verified

d(x*,x)<δd(x*,x(t))<ϵ.

In particular, d(x*,x(0))=0.

TitleLyapunov stable
Canonical nameLyapunovStable
Date of creation2013-03-22 13:06:29
Last modified on2013-03-22 13:06:29
Ownerarmbrusterb (897)
Last modified byarmbrusterb (897)
Numerical id10
Authorarmbrusterb (897)
Entry typeDefinition
Classificationmsc 34D20
SynonymLyapunov stability
SynonymLiapunov stable
SynonymLiapunov stability
Related topicAsymptoticallyStable
Related topicAttractingFixedPoint
Related topicStableFixedPoint
Related topicNeutrallyStableFixedPoint
Related topicUnstableFixedPoint
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