In this paper we address the edge-agreement problem with preserved connectivity for networks of first and second-order systems under proximity constraints and interconnected over a class of directed graphs. We provide a strict Lyapunov function that leads to establishing uniform asymptotic stability of the consensus manifold with guaranteed connectivity preservation. Furthermore, robustness of the edge-agreement protocol, in the sense of input-to-state stability with respect to external input disturbances, is also demonstrated. These results hold for directed-spanning-tree and directed-cycle topologies, which are notably employed, respectively, in leader–follower and cyclic-pursuit control.

在本文中，我们解决了在一阶和二阶系统网络在邻近约束下保持连通性并通过一类有向图互连的边缘一致性问题。我们提供了一个严格的 Lyapunov 函数，它导致在保证连接性保持的情况下建立共识流形的均匀渐近稳定性。此外，还证明了边缘协议协议的鲁棒性，即输入到状态相对于外部输入干扰的稳定性。这些结果适用于有向生成树和有向循环拓扑，它们分别显着用于领导者 - 跟随者和循环追踪控制。