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Exponential stability of time-delay systems via new weighted integral inequalities

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  • Hien, Le Van
  • Trinh, Hieu

Abstract

In this paper, new weighted integral inequalities (WIIs) are first derived based on Jensen’s integral inequalities in single and double forms. It is theoretically shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvement based on Wirtinger’s integral inequality. The potential capability of WIIs is demonstrated through applications to exponential stability analysis of some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

Suggested Citation

  • Hien, Le Van & Trinh, Hieu, 2016. "Exponential stability of time-delay systems via new weighted integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 335-344.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:335-344
    DOI: 10.1016/j.amc.2015.11.076
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Wang, Zhanshan & Ding, Sanbo & Zhang, Huaguang, 2017. "Hierarchy of stability criterion for time-delay systems based on multiple integral approach," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 422-428.
    2. Feng, Yuming & Yang, Xinsong & Song, Qiang & Cao, Jinde, 2018. "Synchronization of memristive neural networks with mixed delays via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 874-887.
    3. R. Saravanakumar & Grienggrai Rajchakit & M. Syed Ali & Young Hoon Joo, 2017. "Extended dissipativity of generalised neural networks including time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(11), pages 2311-2320, August.
    4. Kwon, W. & Koo, Baeyoung & Lee, S.M., 2018. "Novel Lyapunov–Krasovskii functional with delay-dependent matrix for stability of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 149-157.
    5. Ding, Yucai & Liu, Hui & Xu, Hui & Zhong, Shouming, 2019. "On uniform ultimate boundedness of linear systems with time-varying delays and peak-bounded disturbances," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 381-392.
    6. Gyurkovics, É. & Szabó-Varga, G. & Kiss, K., 2017. "Stability analysis of linear systems with interval time-varying delays utilizing multiple integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 164-177.
    7. Sun, Yonghui & Li, Ning & Shen, Mouquan & Wei, Zhinong & Sun, Guoqiang, 2018. "Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 1-11.
    8. Jun-Juh Yan & Hang-Hong Kuo, 2022. "Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays," Mathematics, MDPI, vol. 10(11), pages 1-13, May.
    9. Liu, Yan & Mei, Jingling & Li, Wenxue, 2018. "Stochastic stabilization problem of complex networks without strong connectedness," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 304-315.

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