Distributed consensus of multi-agent systems with finite-level quantization

This paper is concerned with consensus control of undirected networks of discrete time first order agents under quantized communication. A distributed protocol is proposed based on dynamic encoding and decoding with finite level uniform quantizers. It is shown that under the protocol designed, for a connected network, average-consensus can be achieved with an exponential convergence rate based on a single-bit information exchange between each pair of adjacent nodes at each time step. As the number of agents increases, the explicit form of the asymptotic convergence rate is given in relation to the number of nodes, the number of the quantization levels and the ratio between the algebraic connectivity and the spectral radius of the Laplacian of the communication graph.