Quantized consensus on first-order integrator networks

This paper studies the quantized average consensus problem of first-order integrator agents with connected undirected communication graphs. Because quantized data is inherently associated with discrete-time measurements, a sampled-data based average consensus protocol is proposed, in which each agent uses the quantized states of its neighbors measured synchronously at sampling times to update its own state. It is proved that for a connected network, the distance between the individual state and the average of initial states becomes smaller than the quantization step size in finite time, provided the sampling size is smaller than a constant depending on the degree of the communication topology. When the sampling size tends to zero, an asynchronous protocol is investigated, in which the limitation of the switching frequency of quantizers is considered. It is shown that for a connected network, the given protocol drives the state of each agent into a neighborhood of the average of initial states, provided the dwell-time of quantizers is small enough.