  This paper models a class of hierarchical cyber-physical systems and studies
its associated consensus problem. The model has a pyramid structure, which
reflects many realistic natural or human systems. By analyzing the spectrum of
the coupling matrix, it is shown that all nodes in the physical layer can reach
a consensus based on the proposed distributed protocols without interlayer
delays. Then, the result is extended to the case with interlayer delays. A
necessary and sufficient condition for consensus-seeking is derived from the
frequency domain perspective, which describes a permissible range of the delay.
Finally, the application of the proposed model in the power-sharing problem is
simulated to demonstrate the effectiveness and significance of the analytic
results.

Systems and Control;Systems and Control