  Spreading information through a network of devices is a core activity for
most distributed systems. As such, self-stabilizing algorithms implementing
information spreading are one of the key building blocks enabling aggregate
computing to provide resilient coordination in open complex distributed
systems. This paper improves a general spreading block in the aggregate
computing literature by making it resilient to network perturbations,
establishes its global uniform asymptotic stability and proves that it is
ultimately bounded under persistent disturbances. The ultimate bounds depend
only on the magnitude of the largest perturbation and the network diameter, and
three design parameters trade off competing aspects of performance. For
example, as in many dynamical systems, values leading to greater resilience to
network perturbations slow convergence and vice versa.
