Leader-follower controllability of signed networks

This study addresses leader-follower controllability of signed multi-agent networks with fixed and switching interactions (topologies), respectively, where weighted edges between agents may be positive or negative. In other words, there exist cooperative interactions (corresponding to positive edges) and antagonistic interactions (corresponding to negative edges) between agents in the multi-agent networks depicted by signed graphs. The goal of this study is to find the criteria of controllability for signed multi-agent networks, that is, how exactly do cooperation and antagonism affect controllability? It is proven that the followers of multi-agent networks under structurally balanced conditions can be controlled to the desired states if the leaders are chosen from the same partitioned subset. In addition, a signed multi-agent network with simultaneously structurally balanced conditions can be switching controllable even though each subsystem is uncontrollable. The leaders' selection is also discussed.