Quantized consensus for linear discrete-time multi-agent systems

In this paper, we consider distributed consensus of linear discrete-time agents whose states are transmitted through logarithmic quantizer. A distributed consensus protocol is proposed based on the states and outputs of encoders and decoders. Even though every single agent´s system is stabilized, the consensus of whole multi-agent system may still not be achieved. We prove that for some linear discrete-time systems, by selecting the parameters of logarithmic quantizer properly, the asymptotic consensus can be achieved. We also derive the upper bound for the convergence rate of consensus algorithm. A simulation is given to show the feasibility of the proposed consensus protocol.