Pinning Synchronization in Heterogeneous Networks of Harmonic Oscillators

Abstract

In this paper, a networked heterogeneous system coupled of multiple nonidentical harmonic oscillators is investigated. The synchronization problem for the networked heterogeneous system is studied. To synchronize the heterogeneous network, a leader is introduced. Based on the pinning control, a distributed control input is proposed to synchronize the heterogeneous network to the leader. By Lyapunov functional method and matrix theory, sufficient conditions for guaranteeing quasi-synchronization between the heterogeneous network and the leader are obtained. The theoretical results show that all the heterogeneous oscillators can tend eventually to the leader oscillator within a bounded error. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.