Edge-based strict Lyapunov functions for consensus with connectivity preservation over directed graphs

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