Robustness of noisy consensus dynamics with directed communication

Abstract

In this paper we study robustness of consensus in networks of coupled single integrators driven by white noise. Robustness is quantified as the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm of the closed-loop system. In particular we investigate how robustness depends on the properties of the underlying (directed) communication graph. To this end several classes of directed and undirected communication topologies are analyzed and compared. The trade-off between speed of convergence and robustness to noise is also investigated.