Hybrid consensus problems among a group of continuous-time high-order agents with directed communication topology are investigated by a time delay approach, where each agent obtains the communication information from its neighboring agents only at discrete-time instants. Firstly, based on both the continuous-time state information of each agent and the discrete-time communication information with time-varying sampling interval of its neighboring agents, a hybrid discrete/continuous consensus protocol is designed. Secondly, hybrid consensus problems are transformed into simultaneous stabilization problems of multiple sampled control subsystems with low dimensions by the state space decomposition approach. Thirdly, by using the time delay approach and linear matrix inequality (LMI) theory, sufficient conditions for hybrid consensus and consensualization are presented, where four LMI constraints are only included. It should be pointed out that the hybrid consensus for high-order swarm systems depends on the gain matrices, the spectra property of the Laplacian matrix, and the maximum sampling interval. Moreover, the consensus function is determined when swarm systems achieve hybrid consensus. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.
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