Harmonic synchronization under all three types of coupling: Position, velocity, and acceleration

TUNA S. E.

Automatica, vol.130, 2021 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 130
  • Publication Date: 2021
  • Doi Number: 10.1016/j.automatica.2021.109727
  • Journal Name: Automatica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Applied Science & Technology Source, Aqualine, Communication Abstracts, Computer & Applied Sciences, Information Science and Technology Abstracts, INSPEC, Library, Information Science & Technology Abstracts (LISTA), MathSciNet, zbMATH, DIALNET
  • Keywords: Synchronization, Laplacian matrix, Harmonic oscillator, Acceleration coupling, OSCILLATORS, NETWORK
  • Middle East Technical University Affiliated: Yes

Abstract

© 2021 Elsevier LtdSynchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the oscillators asymptotically synchronize if and only if this matrix has a single eigenvalue on the imaginary axis. This result generalizes some of the known spectral tests for synchronization. Some simpler Laplacian constructions are also proved to work provided that certain structural conditions are satisfied by the coupling graphs.