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This paper provides a review of the consensus problem as one of the most challenging issues in the distributed control of the multi-agent systems (MASs). In this survey, firstly, the consensus algorithms for the agents with the single-integrator, double-integrator and high-order dynamic models were collected from various research works, and the convergence condition for each of these algorithms was explained. Secondly, all the consensus-related problems such as those in the sampled-data consensus, quantized consensus, random-network consensus, leader-follower consensus, finite-time consensus, bipartite consensus, group consensus/cluster consensus, and the scaled consensus were analyzed and compared with each other. Thirdly, we focused on the common control techniques used for the consensus problems in the presence of disturbance and divided all these control methods into two categories: robust control and adaptive control. Finally, we reviewed the most prevalent consensus applications in the MASs, including the subjects of rendezvous, formation control, axial alignment and the wireless sensor networks.

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