Characterizing Energy-Related Controllability of Complex Networks Via Cartesian Product

This work investigates energy-related controllability of composite complex networks constructed by factor networks via Cartesian graph product. Particularly, the considered factor networks are leader-follower signed networks with neighbor-based Laplacian dynamics, adopting positive and negative edges to capture cooperative and competitive interactions among network units. Instead of considering classical controllability, energy-related metrics of composite networks capturing system performance, such as average controllability and volumetric control energy, are characterized through their corresponding factor networks. It is revealed that the eigenvalues and eigenvector matrices of factor systems can be used to characterize energy-related controllability of composite networks.