A sufficient condition for k-contraction in Lurie systems

Ron Ofir*, Alexander Ovseevich, Michael Margaliot

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationIFAC-PapersOnLine
EditorsHideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita
PublisherElsevier B.V.
Pages71-76
Number of pages6
Edition2
ISBN (Electronic)9781713872344
DOIs
StatePublished - 1 Jul 2023
Event22nd IFAC World Congress - Yokohama, Japan
Duration: 9 Jul 202314 Jul 2023

Publication series

NameIFAC-PapersOnLine
Number2
Volume56
ISSN (Electronic)2405-8963

Conference

Conference22nd IFAC World Congress
Country/TerritoryJapan
CityYokohama
Period9/07/2314/07/23

Keywords

  • Hopfield network
  • Stability of nonlinear systems
  • bounded real lemma
  • contraction theory
  • kth compound matrices

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