Distributed Consensus of Third-order Multi-agent Systems with Communication Delay

This paper studies the consensus problem for a class of general third-order multi-agent systems on an undirected connected network. By employing a variables transformation, the consensus control problem can be turned into a asymptotical stability problem. Then we present a necessary and sufficient condition for guaranteeing consensus by using Routh-Hurwitz stability criterion. And this result can be applied to a special case of third-order integrator systems. Also we will present a tolerable communication time delay for third-order integrator systems under the assumption that multi-agent systems can reach consensus without communication delay.