Controllability of multi-agent systems coupled by dynamic edges

In this paper, we investigate the controllability properties of a first-order multi-agent coupled with dynamic edges (MADE) system. We provide the necessary and sufficient conditions for the controllability of generic system and homogeneous edges system. Interesting results include that the controllability of homogeneous edges MADE system has strong relationship with the induced multi-agent system. Besides, we propose a necessary condition about the controllability of the general heterogeneous edges MADE system. Also, for the star graph, we propose a sufficient condition to test whether it is controllable.