Consensus of a Group of Second Order Agents with Switching Irregular Communication Topologies and Time-Delay

This study addresses the consensus problem and its stability for a group of agents with second order dynamics and communication delays. The communication topologies under consideration are irregular, i.e., the number of peers each agent communicates with is not fixed across the network. Furthermore, they switch from one topology to another in time. Communication delays are assumed to be quasi-static and they remain the same for all the interagent channels. A decentralized PD-like control structure is proposed to create consensus in the position and velocity of the agents. The proposed control logic introduces an interesting factorization to the characteristic equation of the system. This property brings the stability analysis from a prohibitively large dimension to a small scale, for a considerable efficiency improvement. A complete stability picture is obtained using a recent paradigm named CTCR. The treatment takes into account variations in both the control parameters and the communication delays. Case studies and simulations results are presented to verify the analytical derivations.