On the controllability of single-leader multi-chain systems

This work is concerned with the controllability of the single-leader multi-agent system with the chain structures. It is shown that the multi-chain system evolving according to the consensus policy described by the linear time-invariant model is controllable if and only if the system does not have two chain lengths satisfying some specific pattern. This result improves a recent elegant work on the similar topic, where only a sufficient condition for the system uncontrollability was proposed.