This paper investigates the high-order consensus problem for the multi-agent systems with agent's dynamics described by high-order integrator, and adopts a general consensus algorithm composed of the states' coordination control. Under communication delay, consensus algorithm in usual asynchronously-coupled form just can make the agents achieve a stationary consensus, and sufficient consensus condition is obtained based on frequency-domain analysis. Besides, a predictor-based consensus algorithm is constructed via multiplying the delayed neighboring agents' states by a delay-related compensation part. In our proposed algorithm, a compensating delay is introduced to match the communication delay. Specially, the original high-order consensus is regained when the compensating delay equals to the communication delay, but cannot be achieved if the compensating delay is not equivalent to the communication delay. Moreover, sufficient consensus convergence conditions are also obtained for the agents under our predictor-based algorithm with different compensating delay. Numerical studies for multiple quadrotors illustrate the correctness of our results.
consensus, high-order multi-agent system, communication delay, predictor-based consensus algorithm, multiple quadrotors