Stability Analysis for the Group Dynamics Consensus with Time Delayed Communications

This study addresses the consensus problem for a group of agents with second order dynamics and feedback time delays. It is assumed that all agents have identical capabilities, they communicate with the same number of neighbors, and the time delay in these channels is the same for all the agents. A distributed control structure of PD type is proposed to create consensus in the steady state positions and velocities. This law also introduces a peculiar factorizability feature into the characteristic equation of the system, which assists the stability analysis in the delay space tremendously. A unique, exact and complete stability picture is obtained using CTCR method, under the variations in the control parameters as well as in the communication delay. Case studies and simulation results are presented to verify the analytical derivations.