Bipartite consensus in coupled harmonic oscillators with local instantaneous interaction and measurement noise

Abstract

Abstract This paper investigates the issue of bipartite consensus for coupled harmonic oscillators under the cooperation‐competition network topology while considering measurement noise. The concept of bipartite consensus in mean square is established for networked harmonic oscillator systems. In this sense, two consensus algorithms that only use sampled velocity data on the agents in a network are given. Based on the specific structure of the Laplacian matrix related to the cooperation‐competition network topology, some sufficient conditions are given to ensure the realisation of the bipartite consensus of the coupled harmonic oscillators. Finally, three examples are provided to illustrate the corresponding theoretical results.