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Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma

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  • Dawei Gong
  • Frank L. Lewis
  • Liping Wang
  • Dong Dai
  • Shuang Zhang

Abstract

The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear matrix inequality (LMI) relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control.

Suggested Citation

  • Dawei Gong & Frank L. Lewis & Liping Wang & Dong Dai & Shuang Zhang, 2017. "Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma," Complexity, Hindawi, vol. 2017, pages 1-9, June.
    • Handle: RePEc:hin:complx:2137103
    DOI: 10.1155/2017/2137103
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    References listed on IDEAS

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    1. Dawei Gong & Jinhai Liu & Shuangyu Zhao, 2015. "Chaotic synchronisation for coupled neural networks based on T-S fuzzy theory," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(4), pages 681-689, March.
    2. Fang, Mei, 2015. "Synchronization for complex dynamical networks with time delay and discrete-time information," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 1-11.
    3. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
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