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Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays

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  • Liu, Bin
  • Chen, Guanrong
  • Teo, Kok Lay
  • Liu, Xinzhi

Abstract

In this paper, we aim to study the robust global exponential synchronization problem for a general class of Lur’e chaotic systems subject to time delays and impulsive disturbances. Furthermore, we also provide an estimation of the maximum Lyapunov exponent. By using the Lyapunov function method and linear matrix inequality (LMI) technique, sufficient conditions for the robust global exponential synchronization and estimation of its maximum Lyapunov exponent are obtained for the class of Lur’e chaotic systems with and without time delays, respectively. Furthermore, by applying the M-matrix theory, some of these sufficient conditions are shown to be expressible in forms of fairly simple algebraic conditions. For illustration, several examples are solved by using the sufficient conditions obtained.

Suggested Citation

  • Liu, Bin & Chen, Guanrong & Teo, Kok Lay & Liu, Xinzhi, 2005. "Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1629-1641.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:5:p:1629-1641
    DOI: 10.1016/j.chaos.2004.06.050
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    Cited by:

    1. Zhang, Zhi-Ming & He, Yong & Wu, Min & Wang, Qing-Guo, 2017. "Exponential synchronization of chaotic neural networks with time-varying delay via intermittent output feedback approach," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 121-132.
    2. Yan, Jun-Juh & Lin, Jui-Sheng & Liao, Teh-Lu, 2007. "Robust dynamic compensator for a class of time delay systems containing saturating control input," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1223-1231.
    3. Zhang, Xiaohong & Khadra, Anmar & Yang, Dan & Li, Dong, 2009. "Analysis and design for unified exponential stability of three different impulsive T–S fuzzy systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1559-1566.
    4. Zheng, Juanhui & Cui, Baotong, 2018. "State estimation of chaotic Lurie system with logarithmic quantization," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 141-148.
    5. Song, Qiankun & Cao, Jinde, 2007. "Synchronization and anti-synchronization for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 929-939.
    6. Shen, Liqun & Wang, Mao, 2008. "Robust synchronization and parameter identification on a class of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 106-111.
    7. Liu, Haoliang & Zhang, Taixiang & Li, Xiaodi, 2021. "Event-triggered control for nonlinear systems with impulse effects," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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