  This paper is concerned with the study of synchronization and consensus
phenomena in complex networks of diffusively-coupled nodes subject to external
disturbances. Specifically, we make use of stochastic Lyapunov functions to
provide conditions for synchronization and consensus for networks of nonlinear,
diffusively coupled nodes, where noise diffusion is not just additive but it
depends on the nodes' state. The sufficient condition we provide, wich links
together network topology, coupling strength and noise diffusion, offers two
interesting interpretations. First, as suggested by {\em intuition}, in order
for a network to achieve synchronization/consensus, its nodes need to be
sufficiently well connected together. The second implication might seem,
instead, counter-intuitive: if noise diffusion is {\em properly} designed, then
it can drive an unsynchronized network towards synchronization/consensus.
Motivated by our current research in Smart Cities and Internet of Things, we
illustrate the effectiveness of our approach by showing how our results can be
used to control certain collective decision processes.
