Eigenvector based design of uncontrollable topologies for networks of multiple agents

The paper studies controllability of networks of multiple agents from the viewpoint of topologies construction. Based on Laplacian eigenvector and the leader-follower framework, an approach is proposed to construct new topology structures when an original communication graph is uncontrollable. Leader agents are clearly indicated under which all the constructed topologies are proved to be uncontrollable. As a byproduct the approach leads to a necessary condition on controllability. To enrich understanding of controllability, some necessary and sufficient conditions are also proposed at the end of the paper.