Computation and verification of contraction metrics for periodic orbits

Giesl, Peter, Hafstein, Sigurdur and Mehrabinezhad, Iman (2021) Computation and verification of contraction metrics for periodic orbits. Journal of Mathematical Analysis and Applications, 203 (2). a125309 1-32. ISSN 0022-247X

[img] PDF - Accepted Version
Available under License Creative Commons Attribution-NonCommercial No Derivatives.

Download (3MB)


Exponentially 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 21 May 2021 07:16
Last Modified: 12 May 2022 01:00

View download statistics for this item

📧 Request an update