IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v33y2007i1p156-162.html
   My bibliography  Save this article

Limit cycles design for a class of bilinear control systems

Author

Listed:
  • Sun, Yeong-Jeu

Abstract

In this paper, the feedback control for a class of bilinear control systems is investigated. Using the Bellman–Gronwall inequality, a feedback control is proposed to guarantee the existence of limit cycles for such bilinear control systems. Moreover, the exponentially stable limit cycles, the guaranteed convergence rate, and frequency of oscillation can be correctly estimated. Finally, a numerical example is provided to illustrate the use of the main result.

Suggested Citation

  • Sun, Yeong-Jeu, 2007. "Limit cycles design for a class of bilinear control systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 156-162.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:156-162
    DOI: 10.1016/j.chaos.2006.01.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906000075
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.01.004?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. Cheng, Zunshui & Lin, Yiping & Cao, Jinde, 2006. "Dynamical behaviors of a partial-dependent predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 67-75.
    2. Ramos, J.I., 2006. "Piecewise-linearized methods for oscillators with limit cycles," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1229-1238.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sun, Yeong-Jeu, 2009. "Existence of self-oscillation for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 731-734.

    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. Sun, Yeong-Jeu, 2009. "The existence of the exponentially stable limit cycle for a class of nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2357-2362.
    2. Sun, Yeong-Jeu, 2009. "Existence of self-oscillation for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 731-734.
    3. Sun, Yeong-Jeu, 2008. "Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 89-96.
    4. Singh, Vimal, 2008. "Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 178-183.
    5. Singh, Vimal, 2007. "A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 813-816.
    6. Lv, Jian Cheng & Yi, Zhang, 2007. "Some chaotic behaviors in a MCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1040-1047.
    7. Singh, Vimal, 2007. "Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1448-1453.
    8. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    9. Singh, Vimal, 2008. "Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 677-681.
    10. Ramos, J.I., 2006. "Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1306-1313.

    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:33:y:2007:i:1:p:156-162. 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.