Collective Behaviors of Discrete-Time Multi-Agent Systems Over Signed Digraphs
Zhen‐Hua Zhu, Bin Hu, Zhi‐Hong Guan, Zhao Zhang, Xin‐Ming Cheng
Abstract
This article is concerned with the collective behaviors of discrete-time multi-agent systems with single-integrator dynamics under general signed digraphs, in which each agent iteratively updates its own state based upon the current relative states between itself and its neighbors. By using graph-theoretic, matrix-theoretic, and control-theoretic tools, it is shown that with the step-size suitably selected, the states of all agents always converge. More specifically, all agents reach: 1) bipartite consensus (trivial consensus, respectively) if and only if they are related to a strongly connected signed digraph which is structurally balanced (unbalanced, respectively); 2) interval bipartite consensus (trivial consensus, respectively) if and only if their related signed digraph is quasi-strongly connected and contains a structurally balanced (unbalanced, respectively) rooted subdigraph; and 3) bipartite containment (trivial consensus, respectively) if the signed digraph relevant to them is weakly connected and has at least one structurally balanced vertex (has no structurally balanced vertices, respectively). Numerical examples are finally provided to verify the theoretical findings.