Sign-consensus of linear multi-agent systems over signed graphs

This paper investigates sign-consensus of linear multi-agent systems, that is the signs of all agents' states achieve consensus. The communication network we consider is a signed graph, which consists of both positive and negative edges, representing collaboration and competition interactions, respectively. A state feedback control protocol is proposed to make a group of agents achieve sign-consensus. Moreover, we show by an example that conventional consensus can also be achieved even over signed graphs.