Second-order edge agreement with locally Lipschitz dynamics under digraph via edge Laplacian and ISS method

This paper focuses on the second-order edge agreement problem for nonlinear multi-agent systems with unknown locally Lipschitz dynamics under directed topologies. Based on a novel concept, i.e., the essential edge Laplacian, we derive a model reduction representation of the closed-loop multi-agent system based on the spanning tree subgraph. By using the backstepping design, the original multi-agent system can be remodeled as several interacted subsystems with proven ISS (input-to-state stable) properties. Additionally, the interactions of the interacted subsystems can be explicitly illustrated as a gain-interconnection digraph. With the aid of the ISS cyclic-small-gain theorem, the asymptotic stability of the whole system can be guaranteed. To illustrate the effectiveness of the proposed strategy, simulation results are provided.