Synchronization of Coupled Harmonic Oscillators Using Quantized Sampled Position Data

Abstract

For coupled harmonic oscillators (CHO), the paper studies the synchronization problem by using the quantized current sampled position data. The logarithmic quantizer is adopted here to quantize the information transmitted; thus the quantization error of the sampled position data can be illustrated as the uncertainty according to the sector bound property. On the basis of that, the synchronization problem is converted into the asymptotical stability of the subsystems and even the solving problem of characteristic equation. Some sufficient conditions ensuring the synchronization of CHO are obtained relating to coupling strength, sampling period, and quantizer parameter. The usefulness of the theoretical result is shown by an example at the end.