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Global Uniform Asymptotic Stability Criteria for Linear Uncertain Switched Positive Time-Varying Delay Systems with All Unstable Subsystems

Author

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  • Thaned Rojsiraphisal

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand)

  • Piyapong Niamsup

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Suriyon Yimnet

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

In this paper, the problem of robust stability for a class of linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties is investigated. By establishing suitable time-scheduled multiple copositive Lyapunov-Krasovskii functionals (MCLKF) and adopting a mode-dependent dwell time (MDDT) switching strategy, new delay-dependent sufficient conditions guaranteeing global uniform asymptotic stability of the considered systems are formulated. Apart from past studies that studied switched systems with at least one stable subsystem, in the present study, the MDDT switching technique has been applied to ensure robust stability of the considered systems with all unstable subsystems. Compared with the existing results, our results are more general and less conservative than some of the previous studies. Two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Thaned Rojsiraphisal & Piyapong Niamsup & Suriyon Yimnet, 2020. "Global Uniform Asymptotic Stability Criteria for Linear Uncertain Switched Positive Time-Varying Delay Systems with All Unstable Subsystems," Mathematics, MDPI, vol. 8(12), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2118-:d:451808
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    References listed on IDEAS

    as
    1. Ji-Shi Zhang & Yan-Wu Wang & Jiang-Wen Xiao & Yan-Jun Shen, 2014. "Stability analysis of switched positive linear systems with stable and unstable subsystems," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 2458-2465, December.
    2. Jinjin Liu & Kanjian Zhang & Haikun Wei, 2016. "Robust stability of positive switched systems with dwell time," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(11), pages 2553-2562, August.
    3. Sami Elmadssia & Karim Saadaoui, 2020. "New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
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