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Impulsive control and synchronization of Chua’s oscillators

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  • Sun, Jitao
  • Zhang, Yinping

Abstract

Impulsive control of a chaotic system is ideal for designing digital control schemes where the control laws are generated by digital devices which are discrete in time. In this paper, several new theorems on the stability of impulsive control systems are presented. These theorems are then used to find the conditions under which the Chua’s oscillator can be asymptotically controlled to the origin by using impulsive control. Given the parameters of the Chua’s oscillator and the impulsive control law, an estimation of the upper bound of the impulse interval is given. We also present a theory of impulsive synchronization of two Chua’s oscillators. A numerical example and simulation illustrates the effectiveness of the proposed result. Compared with the existing results, these results are less conservative.

Suggested Citation

  • Sun, Jitao & Zhang, Yinping, 2004. "Impulsive control and synchronization of Chua’s oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 499-508.
    • Handle: RePEc:eee:matcom:v:66:y:2004:i:6:p:499-508
    DOI: 10.1016/j.matcom.2004.03.004
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    References listed on IDEAS

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    1. Sun, Jitao, 2004. "Impulsive control of a new chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(6), pages 669-677.
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    Cited by:

    1. Runzi, Luo & Zhengmin, Wei, 2009. "Adaptive function projective synchronization of unified chaotic systems with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1266-1272.
    2. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.
    3. 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.
    4. Pang, Guoping & Chen, Lansun, 2008. "Dynamic analysis of a pest-epidemic model with impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(1), pages 72-84.
    5. Hung, Yung-Ching & Yan, Jun-Juh & Liao, Teh-Lu, 2008. "Projective synchronization of Chua's chaotic systems with dead-zone in the control input," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 374-382.
    6. Yu, Hengguo & Zhong, Shouming & Ye, Mao, 2009. "Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 619-632.
    7. Wan, Xiaojun & Sun, Jitao, 2011. "Adaptive–impulsive synchronization of chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1609-1617.
    8. Kuo, Hang-Hong & Hou, Yi-You & Yan, Jun-Juh & Liao, Teh-Lu, 2009. "Reliable synchronization of nonlinear chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1627-1635.

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