Controllability analysis of multi-agent systems using relaxed equitable partitions

This paper investigates how to make decentralised networks, amenable to external control, i.e., how to ensure that they are appropriately organised so that they can be effectively 'reprogrammed'. In particular, we study networked systems whose interaction dynamics are given by a nearest-neighbour averaging rule, with one leader node providing the control input to the entire system. The main result is a necessary and sufficient condition for the controllability of such systems in terms of the graph topology. In particular, we give a graph theoretic interpretation of the controllability properties through the so-called relaxed equitable partition.