Open AccessSynchronisation of directed coupled harmonic oscillators with sampled‐data
Author(s) -
Sun Wen,
Lü Jinhu,
Chen Shihua,
Yu Xinghuo
Publication year - 2014
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2013.0849
Subject(s) - control theory (sociology) , harmonic , sampled data systems , harmonic oscillator , computer science , control engineering , physics , control (management) , engineering , artificial intelligence , acoustics , control system , electrical engineering , quantum mechanics
This study investigates the synchronisation problem of instantaneously coupled harmonic oscillators with directed topology. Two distributed algorithms, in which only sampled data are utilised, are proposed for directed coupled harmonic oscillators without and with communication delay, respectively. Necessary and sufficient conditions for achieving synchronised oscillatory motions are established. It is shown that instantaneously coupled harmonic oscillators can be synchronised if and only if each oscillator exchanges the velocity information with its neighbours in an appropriate sampling period which relates to the positive gain, the coupling strength, time delay and the non‐zero eigenvalues of the Laplacian matrix. Simulations are given to illustrate the feasibility of the proposed algorithms.