Synchronization of coupled harmonic oscillators with random noises

This paper investigates synchronization of coupled harmonic oscillators in the presence of random noises under a leaderless framework. Two distributed control algorithms are designed, one for the system with the current feedback information and the other with the delayed feedback information. Sufficient conditions are established which show that synchronization of coupled harmonic oscillators can be achieved almost surely if the Fiedler eigenvalue is larger than a threshold. Simulations are given to illustrate the effectiveness of the proposed distributed control algorithms