Cooperative Behavior of Networked Harmonic Oscillators with Delayed Sampled Position States

This paper investigates the impulsive cooperative behaviors of networked harmonic oscillators by using sampled position states only. A distributed effective algorithm is proposed based on delayed sampled position states over both directed and undirected network topologies. Some necessary and sufficient conditions are established by using the graph theory, ordinary differential equations theory and Schur-Cohn stability criterion. Theoretical results show that the harmonic oscillators can be synchronized if the sampling period fall in an appropriate open interval. Finally, simulations further verify the effectiveness of the theoretical results.