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Global synchronization for a class of dynamical complex networks

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  • Liu, Xian
  • Wang, Jinzhi
  • Huang, Lin

Abstract

This paper is concerned with the problem of global synchronization for a class of dynamical complex networks composed of general Lur’e systems. Based on the absolute stability theory and the Kalman–Yakubovich–Popov (KYP) lemma, sufficient conditions are established to guarantee global synchronization of dynamical networks with complex topology, directed and weighted couplings. Several global synchronization criteria formulated in the form of linear matrix inequalities (LMIs) or frequency-domain inequalities are also proposed for undirected dynamical networks. In order to obtain global results, no linearization technique is involved through derivation of the synchronization criteria. Numerical examples are provided to demonstrate the effectiveness of the proposed results.

Suggested Citation

  • Liu, Xian & Wang, Jinzhi & Huang, Lin, 2007. "Global synchronization for a class of dynamical complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 543-556.
    • Handle: RePEc:eee:phsmap:v:386:y:2007:i:1:p:543-556
    DOI: 10.1016/j.physa.2007.08.029
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    References listed on IDEAS

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    1. Fan, Jin & Li, Xiang & Fan Wang, Xiao, 2005. "On synchronous preference of complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 657-666.
    2. Fan, Jin & Wang, Xiao Fan, 2005. "On synchronization in scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 443-451.
    3. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
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    Cited by:

    1. S. Y. Xu & Y. Yang, 2010. "Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 745-763, September.
    2. Xu, Wei & Wang, Liang & Rong, Haiwu & Li, Dongxi & Niu, Yujun, 2009. "Analysis for the stabilization of impulsive control Liu’s system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1143-1148.
    3. Yang, Xinsong & Huang, Chuangxia & Zhu, Quanxin, 2011. "Synchronization of switched neural networks with mixed delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 817-826.

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