Converse theorem on a contraction metric for a periodic orbit

Peter Giesl

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arXiv · 1808.02689

Converse theorem on a contraction metric for a periodic orbit

Peter Giesl

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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.

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Peter Giesl. 2018-08-08. Converse theorem on a contraction metric for a periodic orbit. https://arxiv.org/abs/1808.02689

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