Edge-based Strict Lyapunov Functions for Consensus with Connectivity Preservation over Directed Graphs

Esteban Restrepo (1, 2) , Antonio Loría (2) , Ioannis Sarras (1) , Julien Marzat (1)

1 DTIS, ONERA, Université Paris Saclay [Palaiseau]
2 L2S - Laboratoire des signaux et systèmes

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.

Mots clés: Consensus; multi-agent systems; synchronisation; Lyapunov methods

Domaines: Sciences de l'ingénieur [physics]; Physique [physics]; Mathématiques [math]; Informatique [cs]

Esteban Restrepo, Antonio Loría, Ioannis Sarras, Julien Marzat. Edge-based Strict Lyapunov Functions for Consensus with Connectivity Preservation over Directed Graphs. Automatica, 2021, 132, pp.109812. ⟨10.1016/j.automatica.2021.109812⟩. ⟨hal-03306580⟩