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Volume 6 Issue 4
Jul.  2019

IEEE/CAA Journal of Automatica Sinica

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Yun Chen and Gang Chen, "Stability Analysis of Systems With Time-varying Delay via a Novel Lyapunov Functional," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1068-1073, June 2019. doi: 10.1109/JAS.2019.1911597
Citation: Yun Chen and Gang Chen, "Stability Analysis of Systems With Time-varying Delay via a Novel Lyapunov Functional," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1068-1073, June 2019. doi: 10.1109/JAS.2019.1911597

Stability Analysis of Systems With Time-varying Delay via a Novel Lyapunov Functional

doi: 10.1109/JAS.2019.1911597
Funds:

the National Natural Science Foundation of China 61703153

the Natural Science Foundation of Hunan Province 2018JJ4075

More Information
  • This paper investigates the stability problem for time-varying delay systems. To obtain a larger delay bound, this paper uses the second-order canonical Bessel-Legendre (B-L) inequality. Secondly, using four couples of integral terms in the augmented Lyapunov-Krasovskii function (LKF) to enhance the relationship between integral functionals and other vectors. Furthermore, unlike the construction of the traditional LKF, a novel augmented LKF is constructed with two new delay-product-type terms, which adds more state information and leads to less conservative results. Finally, two numerical examples are provided to demonstrate the effectiveness and the significant improvement of the proposed stability criteria.

     

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    Highlights

    • The stability problem of time-varying delay systems is investigated.
    • A generalized integral inequality is presented, it can deal with time-varying delay systems without using the reciprocal convexity lemma.
    • A new augmented Lyapunov-Krasovskii function, including four couples of integral terms, is developed.
    • A new delay-product-type Lyapunov-Krasovskii function is given.
    • Two examples are provided to demonstrate the effectiveness and advantage of the proposed approach.

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