Optimal convergence speed with constrained damping of double-integrator multi-agent systems with undirected topology

This papers considers the design of consensus protocols for discrete-time double-integrator multi-agent systems. It provides solutions for the constrained min-max problem, that optimizes the consensus speed subject to a lower bound on damping. It is proven that the damping is determined by the second smallest and largest eigenvalue of the Laplacian of the communication topology only. It is shown that depending on the desired damping value, either analytic solutions for the parameters of the consensus protocol can be provided, or a combined bisection-grid search is required.