Controllability of Leader-Follower Networks with Antagonistic Interactions

Signed networks have been the concern in the network control community as they allow studying antagonistic interactions in multi-agent systems(MASs). In this paper, we mainly address the controllability of a class of signed complete graphs with antagonistic interactions based on the leader-follower structure. The research shows that the leader-follower structure proposed by Tanner (2004) is also applicable to the MASs with antagonistic interactions. We accordingly provide two necessary conditions for the controllability of the system. Particularly, we provide an analysis about the controllability problems of Peterson graphs with antagonistic interactions under the partition of partite graph and give a general conclusion about the controllable subspace. Lastly, some simulations are given to verify the result.