Synchronization of coupled harmonic oscillators with local instantaneous interaction

  • Authors:

  • Jin Zhou;Hua Zhang;Lan Xiang;Quanjun Wu

  • Affiliations:

  • Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China;Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China and Department of Mathematics ...;Department of Physics, School of Science, Shanghai University, Shanghai, 200444, China;Department of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2012

Quantified Score

Hi-index 22.14

Visualization

Abstract

In this brief we propose a distributed algorithm for synchronization of coupled harmonic oscillators with local instantaneous interaction. We provide convergence analysis for such algorithm without and with a leader over fixed and switching undirected network topologies, respectively. We also establish the conditions by which the coupled harmonic oscillators achieve synchronized oscillatory motions under instantaneous network connectivity. It is shown that the coupled harmonic oscillators can be synchronized even each oscillator instantaneously exchanges the velocity information with its neighbors only at discrete moments. Subsequently, numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results.