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Authors: Carlos Argáez 1 ; Peter Giesl 2 and Sigurdur Hafstein 1

Affiliations: 1 Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland ; 2 Department of Mathematics, University of Sussex, Falmer, BN1 9QH, U.K.

ISBN: 978-989-758-442-8

ISSN: 2184-2809

Keyword(s): Complete Lyapunov Functions, Chain-recurrent Set, Numerical Methods, Dynamical Systems, Iterative Methods.

Abstract: A complete Lyapunov function determines the behaviour of a dynamical system. In particular, it splits the phase space into the chain-recurrent set, where solutions show (almost) repetitive behaviour, and the part exhibiting gradient-like flow where the dynamics are transient. Moreover, it reveals the stability of sets and basins of attraction through its sublevel sets. In this paper, we combine two previous methods to compute complete Lyapunov functions: we employ quadratic optimization with equality and inequality constraints to compute a complete Lyapunov function candidate and we evaluate its quality by using a method that improves approximations of complete Lyapunov function candidates through iterations.

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Paper citation in several formats:
Argáez, C.; Giesl, P. and Hafstein, S. (2020). Evaluation of Lyapunov Function Candidates through Averaging Iterations. In Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - ICINCO, ISBN 978-989-758-442-8 ISSN 2184-2809, pages 734-744. DOI: 10.5220/0009992507340744

@conference{icinco20,
author={Carlos Argáez. and Peter Giesl. and Sigurdur Hafstein.},
title={Evaluation of Lyapunov Function Candidates through Averaging Iterations},
booktitle={Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - ICINCO,},
year={2020},
pages={734-744},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009992507340744},
isbn={978-989-758-442-8},
issn={2184-2809},
}

TY - CONF

JO - Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - ICINCO,
TI - Evaluation of Lyapunov Function Candidates through Averaging Iterations
SN - 978-989-758-442-8
IS - 2184-2809
AU - Argáez, C.
AU - Giesl, P.
AU - Hafstein, S.
PY - 2020
SP - 734
EP - 744
DO - 10.5220/0009992507340744

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