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Towards Almost Global Synchronization on the Stiefel Manifold
Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg, Luxembourg.ORCID iD: 0000-0001-6231-9656
Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS).ORCID iD: 0000-0002-9738-4148
Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Luxembourg, Luxembourg.ORCID iD: 0000-0002-5228-6165
2018 (English)In: 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, Dec. 17-19, 2018, Miami Beach, Florida: IEEE, 2018, p. 496-501Conference paper, Published paper (Refereed)
Abstract [en]

The Kuramoto model evolves on the circle, i.e., the 1-sphere S1. A graph G is referred to as S1 -synchronizing if the Kuramoto model on G synchronizes almost globally. This paper generalizes the Kuramoto model and the concept of synchronizing graphs to the Stiefel manifold St (p, n). Previous work on generalizations of the Kuramoto model have largely been influenced by results and techniques that pertain to the original model. It was recently shown that all connected graphs are Sn -synchronizing for all n ≥ 2. However, that does not hold for = 1. Previous results on generalized models may thus have been overly conservative. The n-sphere is a special case of the Stiefel manifold, namely St(1, n+1). As such, it is natural to ask for the extent to which the results on Sn can be extended to the Stiefel manifold. This paper shows that all connected graphs are St(p, n) -synchronizing provided the pair (p, n) satisfies p ≤ [2n/3]-1. © Copyright 2019 IEEE - All rights reserved.

Place, publisher, year, edition, pages
Miami Beach, Florida: IEEE, 2018. p. 496-501
Keywords [en]
Synchronization, dynamical systems, Stiefel manifold, consensus
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:hh:diva-39451DOI: 10.1109/CDC.2018.8619593Scopus ID: 2-s2.0-85062170358OAI: oai:DiVA.org:hh-39451DiVA, id: diva2:1317368
Conference
57th IEEE Conference on Decision and Control (CDC), Miami Beach, Florida, USA, December 17-18, 2018
Note

Financier: Luxembourg University

Available from: 2019-05-22 Created: 2019-05-22 Last updated: 2019-08-16Bibliographically approved

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Markdahl, JohanThunberg, JohanGonçalves, Jorge

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