Sign-Consensus of Linear Multi-Agent Systems Over Signed Directed Graphs

This paper investigates sign-consensus problems of general linear multi-agent systems. The interaction between agents is modeled by a signed directed graph, where both cooperation and competition coexist within a group. The graph is allowed to be structurally unbalanced and its adjacency matrix is assumed to be eventually positive. Distributed control laws are proposed for several classes of graph topologies. Simulation examples are provided to illustrate the proposed control laws. Signed graph-based multi-agent systems provide models to opinion dynamics and social networks, and may also hold significance in further developing such internet search algorithms as PageRank to counter spamming websites.