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Converse theorems on contraction metrics for an equilibrium

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posted on 2023-06-08, 22:59 authored by Peter GieslPeter Giesl
The stability and basin of attraction of an equilibrium can be determined by a contraction metric. A contraction metric is a Riemannian metric with respect to which the distance between adjacent trajectories decreases. The advantage of a contraction metric over, e.g., a Lyapunov function is that the contraction condition is robust under perturbations of the system. While the sufficiency of a contraction metric for the existence, stability and basin of attraction of an equilibrium has been extensively studied, in this paper we will prove converse theorems, showing the existence of several different contraction metrics. This will be useful to develop algorithms for the construction of contraction metrics.

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Publication status

  • Published

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  • Accepted version

Journal

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

Publisher

Elsevier

Issue

2

Volume

424

Page range

1380-1403

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2015-10-29

First Open Access (FOA) Date

2016-05-01

First Compliant Deposit (FCD) Date

2015-10-29

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