Stability Analysis for a Consensus System of a Group of Second Order Dynamics with Time Delays

This study addresses the consensus problem for a group of agents with second order dynamics and time delays. It is assumed that all the agents in the group communicate with each other, and that the time delay incurred is constant and equal for all the communication channels. An efficient control structure of PD type is proposed to create consensus in the position and velocity of the agents. The proposed control law introduces a particular construction into the characteristic equation of the system, which is exploited to simplify the stability analysis in the delay space. A complete stability picture, taking into account the variations in the control parameters and the communication delay, is obtained. Case studies and simulations results are presented to verify the analytical derivations.