Characterization of Collective Behaviors for Directed Signed Networks

This paper targets at exploring how to characterize collective behaviors of directed signed networks. The right eigenvector of the Laplacian matrix associated with zero eigenvalue is further investigated and its mathematical expression is proposed. It is shown that the right eigenvector plays an important role in determining the collective behaviors of directed signed networks. Furthermore, algebraic criteria are introduced for collective behaviors of directed signed networks, such as bipartite consensus, interval bipartite consensus and bipartite containment tracking. In addition, a simulation example is given to the correctness of our developed theoretical results.