Continuous-time consensus dynamics with quantized all-to-all communication

This paper deals with a quantized version of a consensus dynamics in continuous-time, which is motivated by opinion dynamics applications. Under the assumption of all-to-all communication, we show existence and completeness of solutions, we characterize the equilibria, and we prove asymptotical convergence to a state of quantized consensus. For almost all initial conditions, the consensus value differs from the initial average by at most the quantizer precision. Furthermore, we discuss the implications of more general assumptions on the communication graph.