|Title: Convergence bounds for discrete-time second-order multi-agent-systems European Control Conference|
|Written by: Eichler, Annika and Werner, Herbert|
Abstract: This paper presents convergence bounds for discrete-time second-order multi-agent systems with undirected or directed communication graphs. As has been shown before, the convergence depends on the eigenvalues of the Laplace matrix of the communication graph. For each eigenvalue (or eigenvalue pair) analytic bounds for the parameter set are given to render the protocol for that eigenvalue pair stable. In addition it is shown examplarily, that for the case of normalized Laplacian, the stabilizing solution set for the whole topology is non-empty.