Topological Characterizations of Leader-Follower Controllability on Signed Path and Cycle Networks

Leader-follower controllability of signed multiagent networks is investigated in this paper, where the agents interact via neighbor-based Laplacian feedback and the interactions between agents admit positive and negative weights capturing cooperative and competitive interactions. To enable full control of the leader-follower signed network, graph-inspired topological characterizations of the controllability of signed networks are investigated. Specifically, sufficient conditions on the controllability of signed path and cycle networks are developed based on the investigation of the interaction between network topology and agent dynamics. Constructive examples are provided to illustrate how the developed controllability result on signed path and cycle networks can be potentially extended to general signed networks.