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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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.
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    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.

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