摘要：AbstractA graph Laplacian based distributed protocol that can achieve a group consensus over weighted, signed, directed, and weakly connected graphs is investigated. It is said to achieve the group consensus if the state of agents who belong to the same group converges to a common value, while the one of agents who belong to another group converges to a different value. It is assumed that no agent knows which group she belongs to before the protocol is executed. In this paper, for a given signed graph which contains a directed spanning tree, namely, at least one leader that can affect all of the other agents, a definition of n-structurally balanced is proposed. It is emphasized that this definition is a generalization of the structurally balanced which leads a bipartite consensus. Then, necessary and sufficient conditions are established to guarantee the agents’ state reaching the group consensus. The results are illustrated through numerical examples.
