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New technology of synchronization for the uncertain dynamical network with the switching topology

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Abstract

We propose a new technology to synchronize the uncertain dynamical network with the switching topology. In this new technology, we construct the Lyapunov function of network through designing a special function to obtain the network synchronization condition, which effectively avoids the complicated calculations for solving the second largest eigenvalue of the coupling matrix of the dynamical network. At the same time, the uncertain parameters in state equations at network nodes can also be identified accurately by the designed identification laws of uncertain parameters. Our results are universal without assumption about the symmetry of the coupling matrix in network, which can be widely used to research various topologies, no matter whether they are undirected or directed, weighted or unweighted, time-invariant or switching. And there are not any limitations for the synchronization target of network.

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Acknowledgments

This research was supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 2015020079), and the Science and Technology Foundation of Liaoning Provincial Education Department, China (Grant No. L2013410).

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Authors and Affiliations

  1. School of Physics and Electronic Technology, Liaoning Normal University, Dalian, 116029, China

    Ling Lü, Chengren Li, Liansong Chen & Guannan Zhao

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  1. Ling Lü
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  2. Chengren Li
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  3. Liansong Chen
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  4. Guannan Zhao
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Correspondence to Ling Lü.

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Lü, L., Li, C., Chen, L. et al. New technology of synchronization for the uncertain dynamical network with the switching topology. Nonlinear Dyn 86, 655–666 (2016). https://doi.org/10.1007/s11071-016-2913-z

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  • DOI: https://doi.org/10.1007/s11071-016-2913-z

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