We address the consensus problem, with a guarantee of connectivity maintenance, for multiagent systems of first- and second-order, communicating over a connected, undirected graph with proximity constraints. Our approach relies on a so-called barrier Lyapunov functions, which encode the distance constraints between pairs of agents. Beyond the consensus algorithms, our primary contribution is to provide strict barrier Lyapunov functions, i.e. positive definite and with negative definite derivative in the agreement subspace. Thus, uniform asymptotic stability of the consensus manifold and the maintenance of the connectivity are guaranteed. Furthermore, with the said barrier functions, we demonstrate the robustness of consensus protocols by establishing global input-to-state stability.

对于一阶和二阶多智能体系统，我们在保证连通性维护的情况下解决共识问题，通过具有邻近约束的连通无向图进行通信。我们的方法依赖于所谓的障碍 ​​Lyapunov 函数，它对代理对之间的距离约束进行编码。除了共识算法，我们的主要贡献是提供严格的障碍 Lyapunov 函数，即在协议子空间中正定和负定导数。因此，保证了共识流形的一致渐近稳定性和连通性的维护。此外，通过上述障碍函数，我们通过建立全局输入到状态的稳定性来证明共识协议的稳健性。