(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Scaled edge consensus in strongly connected directed multi-agent systems subject to input saturation is examined. Departing from node-based formulations, edge-level dynamics are modeled on the line digraph with heterogeneous scaling, and a fully distributed threshold-based protocol is introduced wherein each edge updates its state using only local disagreements with neighboring edges. Three performance regimes are established: (i) in the unsaturated case, global scaled consensus is achieved; (ii) under saturation, consensus is preserved whenever a verifiable safe dispersion bound on the initial condition holds; and (iii) for large initial disagreements, a low-gain design guarantees bounded quasi-consensus with an explicit radius. The analysis employs Lyapunov methods, Metzler and edge-Laplacian structure, and invariance principles. Simulations on a 10-node, 18-edge directed network corroborate the theory and reveal trade-offs among convergence speed, robustness to saturation, and consensus accuracy. The resulting framework underscores the utility of edge-level coordination under actuation limits and exhibits scalability for networked control, distributed coordination, and edge-centric information processing.