Signal complexity in cyclic consensus systems

In this paper, we deal with classes of LTI cyclic systems from the view point of the information theoretic signal complexity in the networks. The classes contain simple one-layered cyclic systems and hierarchical multi-layered cyclic systems. We firstly give the transfer functions between state variables in the former case and show the entropy of each signal. This result is also discussed in the view point of the channel capacity necessary for the one-layered cyclic systems. We next extend the results to the hierarchical multi-layered cyclic systems. The situation is more complicated and partial results are given. We illustrate the locations of zeros in such cyclic systems from the view point of the structure of the networks.