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Memory feedback PID control for exponential synchronisation of chaotic Lur'e systems

Author

Listed:
  • Ruimei Zhang
  • Deqiang Zeng
  • Shouming Zhong
  • Kaibo Shi

Abstract

This paper studies the problem of exponential synchronisation of chaotic Lur'e systems (CLSs) via memory feedback proportional-integral-derivative (PID) control scheme. First, a novel augmented Lyapunov–Krasovskii functional (LKF) is constructed, which can make full use of the information on time delay and activation function. Second, improved synchronisation criteria are obtained by using new integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. In comparison with existing results, in which only proportional control or proportional derivative (PD) control is used, less conservative results are derived for CLSs by PID control. Third, the desired memory feedback controllers are designed in terms of the solution to linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to show the effectiveness and advantages of the proposed results.

Suggested Citation

  • Ruimei Zhang & Deqiang Zeng & Shouming Zhong & Kaibo Shi, 2017. "Memory feedback PID control for exponential synchronisation of chaotic Lur'e systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(12), pages 2473-2484, September.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:12:p:2473-2484
    DOI: 10.1080/00207721.2017.1322642
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    Cited by:

    1. 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.
    2. M. Hymavathi & Tarek F. Ibrahim & M. Syed Ali & Gani Stamov & Ivanka Stamova & B. A. Younis & Khalid I. Osman, 2022. "Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control," Mathematics, MDPI, vol. 10(20), pages 1-18, October.

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