Leaderless consensus of a hierarchical cyber-physical system

This paper models a class of hierarchical cyber-physical systems and studies its consensus problem. The model has a pyramid structure, reflecting many realistic natural or human systems. By analysing the spectrum of the coupling matrix, it is shown that all nodes in the physical layer can reach 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 developed results.