Contraction metrics for PO 20.05.21.pdf (3.38 MB)
Computation and verification of contraction metrics for periodic orbits
journal contribution
posted on 2023-06-09, 23:55 authored by Peter GieslPeter Giesl, Sigurdur Hafstein, Iman MehrabinezhadExponentially stable periodic orbits of ordinary differential equations and their basins' of attraction are characterized by contraction metrics. The advantages of a contraction metric over a Lyapunov function include its insensitivity to small perturbations of the dynamics and the exact location of the periodic orbit. We present a novel algorithm to rigorously compute contraction metrics, that combines the numerical solving of a first order partial differential equation with rigorous verification of the conditions for a contraction metric. Further, we prove that our algorithm is able to compute a contraction metric for any ordinary differential equation possessing an exponentially stable periodic orbit. We demonstrate the applicability of our approach by computing contraction metrics for three systems from the literature.
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Publication status
- Published
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- Accepted version
Journal
Journal of Mathematical Analysis and ApplicationsISSN
0022-247XPublisher
ElsevierExternal DOI
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2Volume
203Page range
1-32Article number
a125309Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2021-05-21First Open Access (FOA) Date
2022-05-12First Compliant Deposit (FCD) Date
2021-05-20Usage metrics
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