On the controllability of nearest neighbor interconnections

In this paper we derive necessary and sufficient conditions for a group of systems interconnected via nearest neighbor rules, to be controllable by one of them acting as a leader. It is indicated that connectivity seems to have an adverse effect on controllability, and it is formally shown why a path is controllable while a complete graph is not. The dependence of the graph controllability property on the size of the graph and its connectivity is investigated in simulation. Results suggest analytical means of selecting the right leader and/or the appropriate topology to be able to control an interconnected system with nearest neighbor interaction rules.