  In this paper, we provide a theoretical analysis for nonlinear discontinuous
consensus protocols in networks of multiagents over weighted directed graphs.
By integrating the analytic tools from nonsmooth stability analysis and graph
theory, we investigate networks with both fixed topology and randomly switching
topology. For networks with a fixed topology, we provide a sufficient and
necessary condition for asymptotic consensus, and the consensus value can be
explicitly calculated. As to networks with switching topologies, we provide a
sufficient condition for the network to realize consensus almost surely.
Particularly, we consider the case that the switching sequence is independent
and identically distributed. As applications of the theoretical results, we
introduce a generalized blinking model and show that consensus can be realized
almost surely under the proposed protocols. Numerical simulations are also
provided to illustrate the theoretical results.
