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arXiv.org e-Print Archive
Preprint . 2014
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2014
License: arXiv Non-Exclusive Distribution
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Linearization and exponential stability

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2014Embargo end date: 01 Jan 2014Publisher:arXiv
Authors: Zwart, Hans;

doi: 10.48550/arxiv.1404.3475

arXiv: http://arxiv.org/abs/1404.3475

Linearization and exponential stability

Abstract

We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is Fr��chet differential at the equilibrium, if it is only Gateaux differentiable, then we show by means of an example that the result does not hold.

5 pages

Keywords

Mathematics - Functional Analysis, 34G20, 34D20, Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Optimization and Control, Functional Analysis (math.FA)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green