Synchronization of coupled harmonic oscillators with local instantaneous interaction

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.