Weighted network design for practical average consensus in perturbed Multi-Agent Systems

This paper addresses the design of an average consensus control law for perturbed multi-agent systems subject to unknown bounded-in-average disturbances. The consensus strategy is developed for both continuous-time and asynchronous event-triggered implementations. A fully distributed control approach is proposed to ensure practical stability within a specific attractor. The key novelty lies in leveraging projection matrix properties to design the Laplacian weights and triggering parameters through feasible Linear Matrix Inequalities (LMIs). Numerical results validate the theoretical analysis and demonstrate the method's scalability and efficiency, even for large networks with random topologies.