Controllability of Multi-Agent Systems With Cartesian Product Networks

This paper investigates the controllability of Cartesian product networks consisting of smaller factor networks via Cartesian product of graphs, reveals the controllability relationship between the Cartesian product network and its factor networks, and presents a theoretic analysis framework for a Cartesian product network by the eigenvalue-eigenvector pairs of factor networks. A sufficient and necessary condition for the controllability of Cartesian product networks is established based on the PBH test conjoining with the properties of Kronecker products, which is an important theoretical analysis tool to analyze the controllability of product networks. This work will help us to understand the cooperative mechanisms of the system controllability, network topology and nodal dynamics, and provide a theory and technical guidance to build a more reasonable large-scale network model and design an effective control scheme for a real networked system.