Data rate for quantized consensus of high-order multi-agent systems with poles on the unit circle

In this paper, the data rate problem in quantized consensus is considered for a special kind of high-order multi-agent systems. Each agent is in the form of a 2m-th order real Jordan matrix consisting of m pairs of conjugate poles on the unit circle, and only the first state can be measured. Under a connected undirected communication network, a quantized observer-based encoding-decoding scheme is designed and a distributed control law based on the outputs of the encoders and decoders is proposed. With the help of perturbation analysis as well as combinatorial identities, it is shown that the data rate is dependent on the position of the poles and 2m bits of information exchange suffices to achieve the consensus at an exponential convergence rate.