Controllability analysis of multi-agent systems using relaxed equitable partitions

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