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Necessary and sufficient conditions for consensus of third-order discrete-time multi-agent systems in directed networks

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Abstract

This paper studies consensus of third-order discrete-time multi-agent systems in directed networks. When each agent can only receive its neighbor’s position information, necessary and sufficient conditions for consensus of the system are established. Compared with the preceding work, we not only answer what consensus value the system eventually achieves, but also clearly show the equivalent relationship between consensus, scaling parameters and nonzero eigenvalues of the involved Laplacian matrix. Illustrative examples are also given to demonstrate the effectiveness of the obtained theoretical results.

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Acknowledgements

The authors wish to thank the anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, Shandong, 250022, China

    Yanfen Cao & Yuangong Sun

Authors
  1. Yanfen Cao
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  2. Yuangong Sun
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Correspondence to Yuangong Sun.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant Nos. 61473133 and 61374074, and the Natural Science Foundation of Shandong Province under Grant No. JQ201119.

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Cao, Y., Sun, Y. Necessary and sufficient conditions for consensus of third-order discrete-time multi-agent systems in directed networks. J. Appl. Math. Comput. 57, 199–210 (2018). https://doi.org/10.1007/s12190-017-1101-8

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  • DOI: https://doi.org/10.1007/s12190-017-1101-8

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