asymptotically stable
Let be a metric space and a continuous function. A point is said to be Lyapunov stable if for each there is such that for all and all such that , we have .
We say that is asymptotically stable if it belongs to the interior of its stable set, i.e. if there is such that whenever .
In a similar way, if is a flow, a point is said to be Lyapunov stable if for each there is such that, whenever , we have for each ; and is called asymptotically stable if there is a neighborhood of such that for each .
Title | asymptotically stable |
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Canonical name | AsymptoticallyStable |
Date of creation | 2013-03-22 13:55:19 |
Last modified on | 2013-03-22 13:55:19 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 10 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 54H20 |
Classification | msc 37B99 |
Related topic | UnstableFixedPoint |
Related topic | LiapunovStable |
Defines | Lyapunov stable |