The purpose of this short paper is to provide a theoretical analysis for the consensus problem under nonlinear protocols. A main contribution of this work is to generalize the previous consensus problems under nonlinear protocols for networks with un
directed graphs to directed graphs (information flow). Our theoretical result is that if the directed graph is strongly connected and the nonlinear protocol is strictly increasing, then consensus can be realized. Some simple examples are also provided to demonstrate the validity of our theoretical result.
In this paper, without assuming symmetry, irreducibility, or linearity of the couplings, we prove that a single controller can pin a coupled complex network to a homogenous solution. Sufficient conditions are presented to guarantee the convergence of
the pinning process locally and globally. An effective approach to adapt the coupling strength is proposed. Several numerical simulations are given to verify our theoretical analysis.
