Delay dependent criteria for the consensus of second‐order multi‐agent systems subject to communication delay

In this paper, a distributed controller is designed for the consensus of multi‐agent systems in which each agent has a general second‐order linear dynamic and the information is exchanged over a data‐delaying communication network. Using the sensitivity of system poles to the parameters of the control protocol, graphical delay‐dependent synthesis conditions are derived to tune the controller gains. A systematic procedure is developed to attain maximum tolerable transmission delay in the system. Moreover, simpler condition is provided for the special case where the second‐order model is reduced to a double integrator. Simulation results are presented to illustrate the merits of the proposed scheme compared to some recent rival ones in the literature.