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This paper studies the average consensus tracking problem of first-order multi-agent systems under directed topologies. A control protocol is constructed based on the neighbors’ agent sampled information. With the help of the matrix theory and frequency domain analysis, the necessary and sufficient condition can be induced for the average consensus tracking of multi-agent systems, although the weight-balanced condition is not satisfied. In addition, a numerical simulation example is given to illustrate the effectiveness of the proposed results.
Huo et al. (Sun,) studied this question.