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Synchronization of Heterogeneous Partially Coupled Networks with Heterogeneous Impulses

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Abstract

This paper discusses quasi-synchronization problem in an array of heterogeneous partially coupled dynamical networks. At first, based on the Lyapunov stability theorem and the comparison principle, sufficient quasi-synchronization criteria are presented such that the proposed heterogeneous partially coupled dynamical networks with heterogeneous impulses can be synchronized within a nonzero error bound. Then, by taking a specific matrix function, we obtain some lower-dimensional inequalities, which are easy to be verified. Moreover, we propose the design method of controllers under a given error bound and study the optimization problem for the error bound. Finally, a numerical example is provided to illustrate the efficiency of the obtained results.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 61573102, the Natural Science Foundation of Jiangsu Province of China under Grant BK20170019, and the Natural Science Foundation of Zhejiang Province of China under Grant LY15F020018, and China Postdoctoral Science Foundation under Grant No. 2014M560377 and 2015T80483, and Jiangsu Province Six Talent Peaks Project under Grant 2015-ZNDW-002, and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 211189, People’s Republic of China

    Yaqi Wang & Chengdan Ding

  2. Research Center for Complex Systems and Network Science, School of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Jianquan Lu

  3. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jianquan Lu

  4. School of Information Engineering, Huzhou University, Huzhou, 313000, People’s Republic of China

    Jungang Lou

  5. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Fuad E. Alsaadi

  6. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Tasawar Hayat

  7. Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan

    Tasawar Hayat

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  1. Yaqi Wang
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  2. Jianquan Lu
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  3. Jungang Lou
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  4. Chengdan Ding
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Correspondence to Jianquan Lu.

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Wang, Y., Lu, J., Lou, J. et al. Synchronization of Heterogeneous Partially Coupled Networks with Heterogeneous Impulses. Neural Process Lett 48, 557–575 (2018). https://doi.org/10.1007/s11063-017-9735-y

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