IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2011y2011i1n969674.html

Novel Stability Criteria of Nonlinear Uncertain Systems with Time‐Varying Delay

Author

Listed:
  • Yali Dong
  • Shengwei Mei
  • Xueli Wang

Abstract

The problem of robust exponential stabilization for dynamical nonlinear systems with uncertainties and time‐varying delay is considered in the paper. By constructing the proposed Lyapunov‐Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time‐varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time‐varying delays and nonlinear perturbations are derived. Finally, two numerical examples are given to demonstrate the validity of the results.

Suggested Citation

  • Yali Dong & Shengwei Mei & Xueli Wang, 2011. "Novel Stability Criteria of Nonlinear Uncertain Systems with Time‐Varying Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:969674
    DOI: 10.1155/2011/969674
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2011/969674
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/969674?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
    ---><---

    References listed on IDEAS

    as
    1. J. H. Park & S. Won, 1999. "Asymptotic Stability of Neutral Systems with Multiple Delays," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 183-200, October.
    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. Chi-Jo Wang & Juing-Shian Chiou, 2013. "On Delay Independent Stabilization Analysis for a Class of Switched Large‐Scale Time‐Delay Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

    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. Park, Ju H., 2009. "Synchronization of cellular neural networks of neutral type via dynamic feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1299-1304.
    2. J. H. Park & S. M. Lee & H. Y. Jung, 2009. "LMI Optimization Approach to Synchronization of Stochastic Delayed Discrete-Time Complex Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 357-367, November.
    3. K.K. Fan & C.H. Lien & J.G. Hsieh, 2002. "Asymptotic Stability for a Class of Neutral Systems with Discrete and Distributed Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 705-716, September.
    4. Zixin Liu & Shu Lü & Shouming Zhong & Mao Ye, 2009. "Improved Robust Stability Criteria of Uncertain Neutral Systems with Mixed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    5. D. H. Ji & Ju H. Park & S. M. Lee & J. H. Koo & S. C. Won, 2010. "Synchronization Criterion for Lur’e Systems via Delayed PD Controller," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 298-317, November.
    6. O. M. Kwon & J. H. Park & S. M. Lee, 2008. "Exponential Stability for Uncertain Dynamic Systems with Time-Varying Delays: LMI Optimization Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 521-532, June.
    7. Lien, Chang-Hua, 2007. "Delay-dependent and delay-independent guaranteed cost control for uncertain neutral systems with time-varying delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1017-1027.
    8. Liu, Xin-Ge & Wu, Min & Martin, Ralph & Tang, Mei-Lan, 2007. "Delay-dependent stability analysis for uncertain neutral systems with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(1), pages 15-27.
    9. O. M. Kwon & J. H. Park & S. M. Lee, 2010. "An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 343-353, May.
    10. Park, Ju H., 2002. "Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(5), pages 401-412.
    11. He, Shuping & Liu, Fei, 2013. "L2–L∞ fuzzy control for Markov jump systems with neutral time-delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 1-13.
    12. Xiong, Wenjun & Liang, Jinling, 2007. "Novel stability criteria for neutral systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1735-1741.
    13. Mathiyalagan, K. & Vignesh, A., 2026. "A Review on estimation of stability region for nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 516(C).
    14. J. H. Park, 2005. "Delay-Dependent Criterion for Guaranteed Cost Control of Neutral Delay Systems," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 491-502, February.
    15. O. M. Kwon & J. H. Park, 2008. "Exponential Stability for Time-Delay Systems with Interval Time-Varying Delays and Nonlinear Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 277-293, November.

    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:wly:jnlaaa:v:2011:y:2011:i:1:n:969674. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.