Peter Giesl 3-Accepted-8.09.20.pdf (380.36 kB)
On a matrix-valued PDE characterizing a contraction metric for a periodic orbit
The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the position of the periodic orbit and is robust to perturbations. In this paper we characterize such a Riemannian contraction metric as matrix-valued solution of a linear first-order Partial Differential Equation. This enables the explicit construction of a contraction metric by numerically solving this equation in [7]. In this paper we prove existence and uniqueness of the solution of the PDE and show that it defines a contraction metric.
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems - Series B (DCDS-B)ISSN
1531-3492Publisher
American Institute of Mathematical SciencesExternal DOI
Page range
1-27Pages
32.0Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-09-09First Open Access (FOA) Date
2021-10-27First Compliant Deposit (FCD) Date
2020-09-08Usage metrics
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