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Consensus of second-order multi-agent systems with nonlinear dynamics and time delay

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Abstract

This paper aims at investigating the second-order consensus problem of the multi-agent systems with nonlinear dynamics. Since it is more difficult to obtain the velocity information compared with the position information in practical application, a very simple sufficient condition for updating the coupling gain of the velocity information exchange between each agent is firstly derived to achieve asymptotic consensus. Furthermore, communication delay of each agent is considered for velocity information exchange. The velocity signal from a virtual leader is introduced to reach the second-order consensus. All the above fundamental consensus criteria are guaranteed base on algebraic graph theory, matrix theory, and Lyapunov stability method. Two simulation examples are provided to demonstrate the effectiveness of the analytical results. The results obtained in this paper can be easily applied to various cases, which can facilitate practical designs for the second-order consensus.

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Acknowledgments

This work was supported by the National Natural Science and Technology Major Project of China under Grant 2014ZX1004-001-014, the 973 Project under Grant 2014CB845302, the National Natural Science Foundation of China under Grants 61025017, 61174028, 11172215 and 91130022.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China

    Yufeng Qian, Xiaoqun Wu & Jun-an Lu

  2. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Jinhu Lü

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  1. Yufeng Qian
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  2. Xiaoqun Wu
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  3. Jinhu Lü
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  4. Jun-an Lu
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Correspondence to Xiaoqun Wu.

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Qian, Y., Wu, X., Lü, J. et al. Consensus of second-order multi-agent systems with nonlinear dynamics and time delay. Nonlinear Dyn 78, 495–503 (2014). https://doi.org/10.1007/s11071-014-1456-4

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