@inproceedings{3384139cfcf641f0831645a5a2553e0c,
title = "A sufficient condition for k-contraction in Lurie systems",
abstract = "We consider a Lurie system obtained via a connection of a linear time-invariant system and a nonlinear feedback function. Such systems often have more than a single equilibrium and are thus not contractive with respect to any norm. We derive a new sufficient condition for k-contraction of a Lurie system. For k = 1, our sufficient condition reduces to the standard stability condition based on the bounded real lemma and a small gain condition. For k = 2, our condition guarantees well-ordered asymptotic behaviour of the closed-loop system: every bounded solution converges to an equilibrium, which is not necessarily unique. We apply our results to derive a sufficient condition for k-contractivity of a networked system.",
keywords = "Hopfield network, Stability of nonlinear systems, bounded real lemma, contraction theory, kth compound matrices",
author = "Ron Ofir and Alexander Ovseevich and Michael Margaliot",
note = "Publisher Copyright: Copyright {\textcopyright} 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/); 22nd IFAC World Congress ; Conference date: 09-07-2023 Through 14-07-2023",
year = "2023",
month = jul,
day = "1",
doi = "https://doi.org/10.1016/j.ifacol.2023.10.1549",
language = "الإنجليزيّة",
series = "IFAC-PapersOnLine",
publisher = "Elsevier B.V.",
number = "2",
pages = "71--76",
editor = "Hideaki Ishii and Yoshio Ebihara and Jun-ichi Imura and Masaki Yamakita",
booktitle = "IFAC-PapersOnLine",
edition = "2",
}