Average consensus with arbitrarily coarse logarithmic quantizers

This paper considers the average consensus problem for multi-agent systems with continuous-time first-order dynamics. The communication channels among the agents are constrained in which the exchanged information is quantized. In this paper, logarithmic quantization is considered in the communication channels, and sampled-data based protocol is applied. It is shown that as long as the sampling interval is small enough, the consensus protocol is admissible under arbitrarily coarse quantization. To be specific, the consensus error is uniformly bounded and is proportional to the quantization error and averaged initial value. Numerical examples are given to demonstrate the effectiveness of the protocol.