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Converse theorem on a global contraction metric for a periodic orbit
Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions in all directions perpendicular to the ?ow are contracted, then there exists a unique periodic orbit, which is exponentially stable and we obtain an upper bound on the rate of exponential attraction. In this paper we study the converse question and show that, given an exponentially stable periodic orbit, a contraction metric exists on its basin of attraction and we can recover the upper bound on the rate of exponential attraction.
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems - Series AISSN
1078-0947Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
9Volume
39Page range
5339-5363Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-03-20First Open Access (FOA) Date
2020-05-31First Compliant Deposit (FCD) Date
2019-03-19Usage metrics
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