Synchronization of Networked Harmonic Oscillators With Communication Delays Under Local Instantaneous Interaction

Abstract

The primary objective of this paper is to propose a distributed synchronization algorithm in undirected networks of coupled harmonic oscillators having communication delays under local instantaneous interaction. Some generic criteria on exponential convergence for such algorithm over, respectively, undirected fixed and switching network topologies are derived analytically. Different from the existing pure continuous or discrete-time algorithms, a distinctive feature of this work is to solve synchronization problem in undirected networks even if each oscillator instantaneously exchanges the information of the velocity with its neighbors only at some discrete moments. It is shown that the networked harmonic oscillators can be synchronized under instantaneous network connectivity. Subsequently, numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results.