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Impulsive stability of chaotic systems represented by T-S model

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  • Zhang, Xiaohong
  • Khadra, Anmar
  • Li, Dong
  • Yang, Dan

Abstract

In this paper, a novel and unified control approach that combines intelligent fuzzy logic methodology with impulsive control is developed for controlling a class of chaotic systems. We first introduce impulses into each subsystem of T-S fuzzy IF-THEN rules and then present a unified T-S impulsive fuzzy model for chaos control. Based on the new model, a simple and unified set of conditions for controlling chaotic systems is derived by Lyapunov method techniques and a design procedure for estimating bounds on control matrices is also given. These results are shown to be less conservative than those existing ones in the literature and several numerical examples are presented to illustrate the effectiveness of this method.

Suggested Citation

  • Zhang, Xiaohong & Khadra, Anmar & Li, Dong & Yang, Dan, 2009. "Impulsive stability of chaotic systems represented by T-S model," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1863-1869.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1863-1869
    DOI: 10.1016/j.chaos.2008.07.052
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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.
    2. Chen, Bing & Liu, Xiaoping & Tong, Shaocheng, 2007. "Adaptive fuzzy approach to control unified chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1180-1187.
    3. Zhang, Hongbin & Liao, Xiaofeng & Yu, Juebang, 2005. "Fuzzy modeling and synchronization of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 835-843.
    4. Wang, Junwei & Xiong, Xiaohua & Zhao, Meichun & Zhang, Yanbin, 2008. "Fuzzy stability and synchronization of hyperchaos systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 922-930.
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    Cited by:

    1. Kemih, Karim & Kemiha, Adel & Ghanes, Malek, 2009. "Chaotic attitude control of satellite using impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 735-744.
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    4. Harb, Ahmad M. & Smadi, Issam A., 2009. "Tracking control of DC motors via mimo nonlinear fuzzy control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 702-710.

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