Incremental stabilization and multi-agent synchronization of discrete-time nonlinear systems

Samuele Zoboli (1, 2) , Daniele Astolfi (3) , Vincent Andrieu (3) , Giacomo Casadei (4) , Luca Zaccarian (5)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 UT3 - Université Toulouse III - Paul Sabatier
3 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
4 AIS - Ampère, Département Automatique pour l'Ingénierie des Systèmes
5 LAAS - Laboratoire d'analyse et d'architecture des systèmes

In this paper, we propose a novel distributed statefeedback design for robust synchronization of networks of identical discrete-time nonlinear agents under generic time-invariant communication graphs. We focus on the class of almost differentiable (possibly time-varying) dynamics that are linear in the input. By generalizing results on synchronization of linear agents, we build strong links between the solution to the synchronization problem in the linear and nonlinear framework. This is also enabled by the introduction of new results on design of incrementally stabilizing controllers based on contraction analysis. Finally, we propose numerically tractable sufficient conditions for the synchronization of networks of non-smooth Lur'e systems.

Mots clés: Discrete-time nonlinear systems synchronization multi-agent systems contraction incremental stability; Discrete-time; nonlinear systems; synchronization; multi-agent systems; contraction; incremental stability

Domaines: Systèmes et contrôle [cs.SY]; Automatique; Système multi-agents [cs.MA]; Systèmes dynamiques [math.DS]

Samuele Zoboli, Daniele Astolfi, Vincent Andrieu, Giacomo Casadei, Luca Zaccarian. Incremental stabilization and multi-agent synchronization of discrete-time nonlinear systems. 2024. ⟨hal-04444190⟩