IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i3p1559-1566.html
   My bibliography  Save this article

Analysis and design for unified exponential stability of three different impulsive T–S fuzzy systems

Author

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

Abstract

Three different forms of impulsive T–S models are discussed in this paper; the first one is described by a nonlinear impulsive control system represented by T–S model, while the second one is expressed as a state feedback impulsive control plant and the third one is depicted by a hybrid system. A simple and unified Lyapunov-based stability criterion is proposed to guarantee the exponential stability of closed-loop impulsive fuzzy systems. Such criterion is expressed in the form of linear matrix inequalities and the corresponding design algorithms are presented. Several numerical simulations are shown to demonstrate how the proposed controllers can stabilize these impulsive fuzzy systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1559-1566
    DOI: 10.1016/j.chaos.2009.03.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909001581
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.03.036?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Xiaohong & Liao, Xiaofeng & Li, Chuandong, 2005. "Impulsive control, complete and lag synchronization of unified chaotic system with continuous periodic switch," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 845-854.
    2. Yu, Ker-Wei & Lien, Chang-Hua, 2008. "Robust H∞ control for uncertain T–S fuzzy systems with state and input delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 150-156.
    3. Dong, Yuewu & Sun, Jitao, 2005. "Robust stochastic stability and H∞ performance for a class of uncertain impulsive stochastic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1491-1498.
    4. Li, Li & Liu, Xiaodong, 2009. "New approach on robust stability for uncertain T–S fuzzy systems with state and input delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2329-2339.
    5. Chen, Bing & Liu, Xiaoping & Tong, Shaocheng, 2008. "Robust fuzzy control of nonlinear systems with input delay," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 894-901.
    6. Lien, Chang-Hua & Yu, Ker-Wei & Chang, Deng-Hong & Chen, Wei-Da & Wan, Zhao-Lin & Chung, Yeong-Jay & Lu, Ming-Cheng, 2009. "H∞ control for uncertain Takagi–Sugeno fuzzy systems with time-varying delays and nonlinear perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1426-1439.
    7. 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.
    8. 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.
    9. Zhang, Hongbin & Liao, Xiaofeng & Yu, Juebang, 2005. "Fuzzy modeling and synchronization of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 835-843.
    10. Zhong, Qishui & Bao, Jingfu & Yu, Yongbin & Liao, Xiaofeng, 2009. "Exponential stabilization for discrete Takagi–Sugeno fuzzy systems via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2123-2127.
    11. 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.
    12. Zheng, Yongai & Chen, Guanrong, 2009. "Fuzzy impulsive control of chaotic systems based on TS fuzzy model," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 2002-2011.
    13. Chen, Dilan & Sun, Jitao & Huang, Changshui, 2006. "Impulsive control and synchronization of general chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 213-218.
    14. Lien, Chang-Hua, 2007. "Stabilization for uncertain Takagi–Sugeno fuzzy systems with time-varying delays and bounded uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 645-652.
    15. 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.
    16. Lien, Chang-Hua & Yu, Ker-Wei, 2008. "Robust control for Takagi–Sugeno fuzzy systems with time-varying state and input delays," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 1003-1008.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. C. H. Lien & K. W. Yu, 2008. "Robust Reliable Control for Uncertain Time-Delay Systems with IQC Performance," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 235-251, August.
    3. 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.
    4. Zhong, Qishui & Bao, Jingfu & Yu, Yongbin & Liao, Xiaofeng, 2009. "Exponential stabilization for discrete Takagi–Sugeno fuzzy systems via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2123-2127.
    5. Zheng, Yongai & Chen, Guanrong, 2009. "Fuzzy impulsive control of chaotic systems based on TS fuzzy model," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 2002-2011.
    6. Yu, Ker-Wei & Lien, Chang-Hua, 2008. "Robust H∞ control for uncertain T–S fuzzy systems with state and input delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 150-156.
    7. Yang, Xinsong & Huang, Chuangxia & Zhu, Quanxin, 2011. "Synchronization of switched neural networks with mixed delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 817-826.
    8. Feng, Yuhu & Hu, Liangjian, 2006. "On the quasi-controllability of continuous-time dynamic fuzzy control systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 177-188.
    9. Liu, Yang & Zhao, Shouwei, 2011. "T–S fuzzy model-based impulsive control for chaotic systems and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2507-2516.
    10. 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.
    11. Wu, Xiaoqun & Wang, Jinjun & Lu, Jun-an & Iu, Herbert H.C., 2007. "Hyperchaotic behavior in a non-autonomous unified chaotic system with continuous periodic switch," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1485-1490.
    12. Khastan, A. & Ivaz, K., 2009. "Numerical solution of fuzzy differential equations by Nyström method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 859-868.
    13. Li, Li & Liu, Xiaodong, 2009. "New approach on robust stability for uncertain T–S fuzzy systems with state and input delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2329-2339.
    14. Xu, Wei & Wang, Liang & Rong, Haiwu & Li, Dongxi & Niu, Yujun, 2009. "Analysis for the stabilization of impulsive control Liu’s system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1143-1148.
    15. Senouci, Abdelkader & Boukabou, Abdelkrim, 2014. "Predictive control and synchronization of chaotic and hyperchaotic systems based on a T–S fuzzy model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 62-78.
    16. Liu, Haoliang & Zhang, Taixiang & Li, Xiaodi, 2021. "Event-triggered control for nonlinear systems with impulse effects," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    17. Zheng, Yongai & Ji, Zhilin, 2016. "Predictive control of fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 307-313.
    18. 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.
    19. El-Dessoky, M.M., 2009. "Synchronization and anti-synchronization of a hyperchaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1790-1797.
    20. Coelho, Leandro dos Santos & Araujo, Ernesto, 2009. "Identification of the Hénon chaotic map by fuzzy modeling and Nelder–Mead simplex method," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2762-2772.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1559-1566. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.