Second-order consensus of multi-agent systems in the cooperation–competition network with switching topologies: A time-delayed impulsive control approach

This paper investigates the consensus problem of second-order multi-agent systems with switching topologies by designing a time-delayed impulsive consensus control scheme. All the agents are governed by the same nonlinear intrinsic dynamics. In this study, agents can cooperate or compete with each other, i.e., the elements in the weight matrix of the coupling graph can be either positive or negative. By establishing a comparison system, a new comparison principle method is successfully applied to study such consensus problem. Then, several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree. Meanwhile, the exponential consensus rate is also obtained. Finally, simulation results are presented to validate the effectiveness of the theoretical analysis.