Converse theorem on a contraction metric for a periodic orbit
Dynamical Systems
2018-08-09 v1
Abstract
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 flow are contracted, then there exists a unique periodic orbit, which is exponentially stable and we obtain a 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 bound on the rate of exponential attraction.
Keywords
Cite
@article{arxiv.1808.02689,
title = {Converse theorem on a contraction metric for a periodic orbit},
author = {Peter Giesl},
journal= {arXiv preprint arXiv:1808.02689},
year = {2018}
}