IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v284y2016icp24-36.html
   My bibliography  Save this article

Absolute exponential L1-gain analysis and synthesis of switched nonlinear positive systems with time-varying delay

Author

Listed:
  • Zhang, Junfeng
  • Zhao, Xudong
  • Cai, Xiushan

Abstract

This paper investigates absolute exponential stability and stabilization with L1-gain performance of switched nonlinear positive systems with time-varying delay. Nonlinear functions considered in the paper are located in a sector field and the time-varying delay is unknown but bounded. The notion of absolute exponential L1 stability of switched nonlinear positive systems is first introduced. A nonlinear Lyapunov–Krasovskii functional is constructed for the underlying systems. By using the Lyapunov–Krasovskii functional, a sufficient condition for absolute exponential L1 stability of the systems is established in terms of linear programming. Then, absolute exponential L1 control synthesis of the systems is addressed. A feedback control law containing nonlinear functions and a state-feedback control law are designed, respectively. By comparing with existing results, it is shown that the present design is less conservative. Finally, an illustrative example is provided to illustrate the effectiveness of the results.

Suggested Citation

  • Zhang, Junfeng & Zhao, Xudong & Cai, Xiushan, 2016. "Absolute exponential L1-gain analysis and synthesis of switched nonlinear positive systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 24-36.
    • Handle: RePEc:eee:apmaco:v:284:y:2016:i:c:p:24-36
    DOI: 10.1016/j.amc.2016.02.050
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316301692
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.02.050?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. Li, Erpeng & Long, Lijun & Zhao, Jun, 2015. "Global output-feedback stabilization for a class of switched uncertain nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 551-564.
    2. Yanhui Tong & Lixian Zhang & Peng Shi & Changhong Wang, 2013. "A common linear copositive Lyapunov function for switched positive linear systems with commutable subsystems," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(11), pages 1994-2003.
    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. Xie, Jiyang & Zhu, Shuqian & Feng, Jun-e, 2020. "Delay-dependent and decay-rate-dependent conditions for exponential mean stability and non-fragile controller design of positive Markov jump linear systems with time-delay," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Chen, Xiaoming & Chen, Mou & Qi, Wenhai & Shen, Jun, 2016. "Dynamic output-feedback control for continuous-time interval positive systems under L1 performance," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 48-59.
    3. Li, Shuo & Xiang, Zhengrong, 2020. "Positivity, exponential stability and disturbance attenuation performance for singular switched positive systems with time-varying distributed delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    4. Shitao Zhang & Peng Lin & Junfeng Zhang, 2022. "Event-Triggered Asynchronous Filter of Nonlinear Switched Positive Systems with Output Quantization," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    5. Sun, Yuangong & Tian, Yazhou, 2022. "Polynomial stability of positive switching homogeneous systems with different degrees," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    6. Li, Lei & Qi, Wenhai & Chen, Xiaoming & Kao, Yonggui & Gao, Xianwen & Wei, Yunliang, 2018. "Stability analysis and control synthesis for positive semi-Markov jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 363-375.
    7. Xi, Qiang & Liu, Xinzhi, 2020. "Mode-dependent impulsive control of positive switched systems: Stability and L1-gain analysis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

    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. Yao, Hejun & Gao, Fangzheng & Huang, Jiacai & Wu, Yuqiang, 2021. "Global prescribed-time stabilization via time-scale transformation for switched nonlinear systems subject to switching rational powers," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    2. Jun Shen & James Lam, 2015. "On ℓ and gains for positive systems with bounded time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 1953-1960, August.
    3. Yan, Xuehua & Song, Xinmin & Wang, Zhonghua & Zhang, Yun, 2017. "Global Output-Feedback Adaptive Stabilization for Planar Nonlinear Systems with Unknown Growth Rate and Output Function," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 299-309.
    4. Ju, Xinxu & Jia, Xianglei & Shi, Xiaocheng & Yu, Shan’en, 2022. "Adaptive output feedback event-triggered tracking control for nonlinear systems with unknown control coefficient," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    5. Shi, Shuang & Fei, Zhongyang & Shi, Zhenpeng & Ren, Shunqing, 2018. "Stability and stabilization for discrete-time switched systems with asynchronism," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 520-536.
    6. Song, Zhibao & Li, Ping & Zhai, Junyong & Wang, Zhen & Huang, Xia, 2020. "Global fixed-time stabilization for switched stochastic nonlinear systems under rational switching powers," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    7. Junfeng Zhang & Zhengzhi Han & Fubo Zhu, 2015. "-gain analysis and control synthesis of positive switched systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2111-2121, September.
    8. Chunbin Qin & Huaguang Zhang & Yanhong Luo & Binrui Wang, 2014. "Finite horizon optimal control of non-linear discrete-time switched systems using adaptive dynamic programming with ε-error bound," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1683-1693, August.
    9. Gisela Pujol-Vazquez & Saleh Mobayen & Leonardo Acho, 2020. "Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation," Mathematics, MDPI, vol. 8(12), pages 1-15, November.

    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:apmaco:v:284:y:2016:i:c:p:24-36. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.