Hierarchical network synthesis for output consensus by eigenvector-based interlayer connections

In this paper, we study consensus problem for hierarchical multi-agent dynamical systems with low rank interconnection by eigenvector-based connection. The system considered is more general than the existing one in a sense that the number of agents in each subsystem and the connection structure of each subsystem are allowed to be different from each other. We provide analytical expressions of the eigenvalue sets of the hierarchical interconnection matrices and systematic synthesis procedures for achieving the output consensus with Lyapunov stability. The results are applicable to more general class of hierarchical interconnection structures than previous work, and numerical examples with simulations confirm the effectiveness of the proposed design method.