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Exponential synchronization of Lur’e complex dynamical networks with uncertain inner coupling and pinning impulsive control

Author

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  • Rakkiyappan, R.
  • Velmurugan, G.
  • Nicholas George, J.
  • Selvamani, R.

Abstract

This paper is concerned with the exponential synchronization of Lur’e type complex dynamical networks with uncertain coupling strength. A novel pinning impulsive controller is designed to achieve synchronization, in which, only selection of nodes are chosen to control instead of the whole network. In addition, the proposed control scheme is digital and it can lead to low installation cost and less time. In order to realize synchronization of Lur’e type complex dynamical networks, crucial delay-dependent stability conditions are derived by utilizing Lyapunov functional together with information of the time-varying delay and convex combination technique. The resulting stability conditions are formulated in the form of linear matrix inequalities (LMIs) and by solving the obtained LMIs, desired impulsive control gain matrices are calculated, which are capable to guarantee the exponential stability of error system. Finally, the effectiveness of the proposed method is demonstrated through numerical simulations.

Suggested Citation

  • Rakkiyappan, R. & Velmurugan, G. & Nicholas George, J. & Selvamani, R., 2017. "Exponential synchronization of Lur’e complex dynamical networks with uncertain inner coupling and pinning impulsive control," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 217-231.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:217-231
    DOI: 10.1016/j.amc.2017.02.041
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    References listed on IDEAS

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    1. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Synchronization in complex delayed dynamical networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 684-692.
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    Cited by:

    1. Yang, Huilan & Wang, Xin & Shu, Lan & Zhao, Guozhu & Zhong, Shouming, 2019. "A new sampling interval fragmentation approach to synchronization of chaotic Lur’e systems," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 12-24.
    2. Feng, Yuming & Yang, Xinsong & Song, Qiang & Cao, Jinde, 2018. "Synchronization of memristive neural networks with mixed delays via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 874-887.
    3. Yang, Huilan & Wang, Xin & Zhong, Shouming & Shu, Lan, 2018. "Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 75-85.
    4. Yiping Luo & Yuejie Yao, 2019. "Finite-Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling," Complexity, Hindawi, vol. 2019, pages 1-14, December.
    5. Nirvin, Prasath & Rihan, Fathalla A. & Rakkiyappan, Rajan & Pradeep, Chandrasekar, 2022. "Impulsive sampled-data controller design for synchronization of delayed T–S fuzzy Hindmarsh–Rose neuron model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 588-602.
    6. Zeng, Deqiang & Zhang, Ruimei & Liu, Yajuan & Zhong, Shouming, 2017. "Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 34-46.
    7. Fei Wang & Zhaowen Zheng & Yongqing Yang, 2019. "Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event-Triggered Control: The Threshold Function Method," Complexity, Hindawi, vol. 2019, pages 1-17, December.

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