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Stability analysis of systems with time-varying delay via novel augmented Lyapunov–Krasovskii functionals and an improved integral inequality

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  • Long, Fei
  • Jiang, Lin
  • He, Yong
  • Wu, Min

Abstract

Delay-dependent stability analysis of linear systems with a time-varying delay is investigated in this paper. Firstly, instead of developing a Lyapunov–Krasovskii functional (LKF) including augmented non-integral quadratic terms as usual, this paper proposes two augmented-integral-function based LKFs, which can reflect closer relationships among system states. Secondly, to bound the derivative of LKF more accurately, a new integral inequality with several free matrices is developed. Compared with the free-matrix-based integral inequality, this inequality can provide additional freedom due to the free matrices introduced. Then, by employing those LKFs and the improved integral inequality, several delay-dependent stability criteria are established for two types of delays. Finally, two numerical examples are given to demonstrate the superiority of the proposed method.

Suggested Citation

  • Long, Fei & Jiang, Lin & He, Yong & Wu, Min, 2019. "Stability analysis of systems with time-varying delay via novel augmented Lyapunov–Krasovskii functionals and an improved integral inequality," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 325-337.
    • Handle: RePEc:eee:apmaco:v:357:y:2019:i:c:p:325-337
    DOI: 10.1016/j.amc.2019.04.004
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    References listed on IDEAS

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    1. 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.
    2. Lee, Seok Young & Lee, Won Il & Park, PooGyeon, 2017. "Improved stability criteria for linear systems with interval time-varying delays: Generalized zero equalities approach," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 336-348.
    3. 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.
    4. Zhang, Ruimei & Zeng, Deqiang & Zhong, Shouming & Yu, Yongbin, 2017. "Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 57-74.
    5. 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.
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    Cited by:

    1. Zhang, Bao-Lin & Cheng, Luhua & Pan, Kejia & Zhang, Xian-Ming, 2020. "Reducing conservatism of stability criteria for linear systems with time-varying delay using an improved triple-integral inequality," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. de Oliveira, Fúlvia S.S. & Souza, Fernando O., 2020. "Further refinements in stability conditions for time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    3. Wang, Chen-Rui & He, Yong & Lin, Wen-Juan, 2021. "Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method," Applied Mathematics and Computation, Elsevier, vol. 391(C).

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