Consensus tracking for first-order agent dynamics with distributed delay

This manuscript explores the consensus tracking problem for first-order continuous agent models over an undirected network, and two categories of distributed delays in the communication are addressed respectively. When the delay postpones the relative information, a permitted delay bound is provided to ensure consensus. Especially, conditions guaranteeing average consensus are provided for integrator systems. Furthermore, consensus conditions are also shown if the distributed delay impacts the neighbours' transmitted information. In the end, two numerical experiments are supplemented to verify the correctness of the derived results.