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Cluster synchronization in nonlinear complex networks under sliding mode control

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Abstract

This paper investigates the cluster synchronization for network of nonlinear systems via differential mean value theorem method and sliding mode control strategy. Because of the existence of the nonlinear dynamics, the differential mean value theorem method is used to transform the nonlinear error complex network system into a linear parameter-varying system. Since the robustness to the uncertainties of the sliding mode, we can deal with the linear parameter-varying system which contains the time-varying mismatched uncertainties by applying the sliding mode control strategy through the equivalent transformation. In addition, appropriate linear matrix inequality stability condition by the Lyapunov method is derived such that each subsystem in the new sliding mode is completely invariant to both matched and mismatched uncertainties. Finally, simulation example is shown to illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Institute of System Science, Northeastern University, Shenyang, 110819, Liaoning Province, China

    Huazhou Hou & Qingling Zhang

  2. Key Laboratory of Networked Control Systems, Chinese Academy of Sciences, Beijing, 110016, China

    Meng Zheng

Authors
  1. Huazhou Hou
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  2. Qingling Zhang
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  3. Meng Zheng
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Correspondence to Qingling Zhang.

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Hou, H., Zhang, Q. & Zheng, M. Cluster synchronization in nonlinear complex networks under sliding mode control. Nonlinear Dyn 83, 739–749 (2016). https://doi.org/10.1007/s11071-015-2363-z

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  • DOI: https://doi.org/10.1007/s11071-015-2363-z

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