Synchronization of Networked Harmonic Oscillators via Quantized Sampled Velocity Feedback

In this article, we propose a practicable quantized sampled velocity data coupling protocol for synchronization of a set of harmonic oscillators. The coupling protocol is designed in a quantized way via interconnecting the velocities encoded by a uniform quantizer with a zooming parameter in either a fixed or an adjustable form over a directed communication network. By constructing a suitable norm to measure the convergence of the synchronization errors, we establish sufficient conditions for the networked harmonic oscillators to converge to a bounded neighborhood of the synchronized orbits with a fixed zooming parameter. The oscillators are ensured to achieve synchronization by designing the quantized coupling protocol with an adjustable zooming parameter. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed coupling protocols.