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Distributed consensus with data rate constraint is an important researchtopic of multi-agent systems. Some results have been obtained for consensus ofmulti-agent systems with integrator dynamics, but it remains challenging forgeneral high-order systems, especially in the presence of unmeasurable states.In this paper, we study the quantized consensus problem for a special kind ofhigh-order systems and investigate the corresponding data rate required forachieving consensus. The state matrix of each agent is a 2m-th order realJordan block admitting m identical pairs of conjugate poles on the unit circle;each agent has a single input, and only the first state variable can bemeasured. The case of harmonic oscillators corresponding to m=1 is firstinvestigated under a directed communication topology which contains a spanningtree, while the general case of m >= 2 is considered for a connected andundirected network. In both cases it is concluded that the sufficient number ofcommunication bits to guarantee the consensus at an exponential convergencerate is an integer between $m$ and $2m$, depending on the location of thepoles.

Data Rate for Distributed Consensus of Multi-agent Systems with High Order Oscillator Dynamics