Abstract
Controllability is a fundamental problem in the study of multi-agent systems. In this paper, we consider the controllability of multi-agent networks, where a collection of agents obey the role of leaders, while the rest of the agents enforce local, consistent protocols. Our goal is to determine the concept of graph theory as a reflection of the theoretical properties of such systems. In particular, we expand the controllability graphical to a multi-leader setting by taking advantage of network almost equitable partitions. We do some analysis and discussions about the existing conclusions and point out the limitation of equitable partitioning method in the study of multi-agent controllability. Besides, we found a class of controllable topology structures and presented a concise proof.
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