Consensus and Synchronized Periodicity in Nonlinear Delayed Networks

In this paper, we investigate stability and convergence properties of a class of nonlinear delayed consensus networks. Using tools and techniques from functional differential equations, sufficient stability conditions with respect to a common state as well as estimates on the convergence rate are derived. We characterize the limit (consensus) state for time-invariant sub-classes of these networks. More importantly, we specify under what conditions a delayed network exhibits periodic synchronized solutions. We provide sufficient conditions for existence, uniqueness and stability of this interesting phenomenon that we illustrate with a simulation example.