IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i21p2763-d669123.html
   My bibliography  Save this article

Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations

Author

Listed:
  • Chang-Hua Lien

    (Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan)

  • Hao-Chin Chang

    (Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan)

  • Ker-Wei Yu

    (Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan)

  • Hung-Chi Li

    (Ph.D. Program of Maritime Science and Technology, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan)

  • Yi-You Hou

    (Department of Intelligent Commerce, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan)

Abstract

In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are used to guarantee the stability and reachable set of the uncertain system with slow variation interval time-varying delay. The mixed performance ( H 2 / H ∞ ) can be derived in the same formulation simultaneously. The design scheme of robust switched control is also developed in this paper. The gains of the controller can be designed and switched to achieve stabilization and mixed performance of the system according to the delay value. Some comparisons with published results are made to show the main contribution of the proposed approach. Finally, some numerical examples are illustrated to show the main results.

Suggested Citation

  • Chang-Hua Lien & Hao-Chin Chang & Ker-Wei Yu & Hung-Chi Li & Yi-You Hou, 2021. "Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2763-:d:669123
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/21/2763/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/21/2763/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hao Chen, 2015. "Improved Results on Reachable Set Bounding for Linear Delayed Systems with Polytopic Uncertainties," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-11, May.
    2. Nguyen D. That & Phan T. Nam & Q. P. Ha, 2013. "Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 96-107, April.
    3. Guoxin Chen & Zhengrong Xiang & Hamid Reza Karimi, 2013. "Observer-Based Robust Control for Switched Stochastic Systems with Time-Varying Delay," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, September.
    4. Chang-Hua Lien & Ker-Wei Yu & Hao-Chin Chang, 2018. "Robust mixed performance switching control for uncertain discrete switched systems with time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(10), pages 2144-2154, July.
    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. Shenping Xiao & Jin Yu & Simon X. Yang & Yongfeng Qiu, 2022. "Stability Analysis for Time-Delay Systems via a New Negativity Condition on Quadratic Functions," Mathematics, MDPI, vol. 10(17), pages 1-9, August.

    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. Trinh, H. & Nam, Phan T. & Pathirana, Pubudu N. & Le, H.P., 2015. "On backwards and forwards reachable sets bounding for perturbed time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 664-673.
    2. Yucai Ding & Hui Liu, 2018. "Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems," Complexity, Hindawi, vol. 2018, pages 1-10, June.
    3. Chengdan Wang & Hongli Yang & Ivan Ganchev Ivanov, 2023. "Controlled Invariant Sets of Discrete-Time Linear Systems with Bounded Disturbances," Mathematics, MDPI, vol. 11(15), pages 1-16, August.
    4. Yuangong Sun & Fanwei Meng, 2017. "Reachable Set Estimation for a Class of Nonlinear Time-Varying Systems," Complexity, Hindawi, vol. 2017, pages 1-6, July.
    5. Deng, Yalin & Zhang, Huasheng & Dai, Yuzhen & Li, Yuanen, 2022. "Interval stability/stabilization for linear stochastic switched systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    6. Wei Kang & Hao Chen & Kaibo Shi & Jun Cheng, 2018. "Further Results on Reachable Set Bounding for Discrete-Time System with Time-Varying Delay and Bounded Disturbance Inputs," Complexity, Hindawi, vol. 2018, pages 1-11, March.
    7. Xingao Zhu & Yuangong Sun, 2019. "Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance," Complexity, Hindawi, vol. 2019, pages 1-6, July.
    8. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Zhen & Wang, Jian, 2020. "Reachable set estimation for Markov jump LPV systems with time delays," Applied Mathematics and Computation, Elsevier, vol. 376(C).

    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:gam:jmathe:v:9:y:2021:i:21:p:2763-:d:669123. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.