Sampled-data based average consensus with logarithmic quantizers

This paper considers the sampled-data average consensus problem for multi-agent systems with first order continuous dynamics. The communication channels among the agents are constrained in which the exchanged information is digital rather than analogue. In this paper, the logarithmic quantizer is applied to the communication channels. A distributed consensus protocol is proposed based on sampled measurements. It is proved that as long as the quantization levels are dense enough, the proposed protocol is robust to the logarithmic quantization, i.e. all the states of the agents are uniformly bounded and the gap between the state of each agent and the average value of the initial conditions converges to zero as the density of quantization levels goes to infinity. An example is given to demonstrate the effectiveness of the protocol.