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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.