Impulsive consensus of multi‐agent directed networks with nonlinear perturbations

SUMMARY This paper investigates the consensus problem of a multi‐agent directed network with nonlinear perturbations (MNNP). Our main objective is to study how the nonlinear perturbations affect a consensus of a multi‐agent network. Based on a reduced‐order transformation, it is shown that an MNNP cannot reach a consensus under a hypothesis even though the discussed network has a spanning tree. The hypothesis shows a detailed relationship between the nonlinear perturbations and the structure of the multi‐agent network. An impulsive approach is then introduced, and a simple criterion is presented to guarantee the consensus of all agents for an MNNP. Finally, a numerical example is provided to illustrate the effectiveness of the obtained criterion.