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Reducing conservatism of stability criteria for linear systems with time-varying delay using an improved triple-integral inequality

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  • Zhang, Bao-Lin
  • Cheng, Luhua
  • Pan, Kejia
  • Zhang, Xian-Ming

Abstract

This paper focuses on stability analysis of linear systems with time-varying delay, where two cases of the time-varying delay are discussed, that is, the time-varying delay is either differentiable or just uniformly continuous. First, an improved triple-integral inequality is proposed to estimate triple-integrals tightly. Then, by introducing two novel Lyapunov–Krasovskii functionals catering for two cases of time-varying delay, two sufficient conditions on stability, respectively, for the system under two cases of time-varying delay are derived using the improved triple-integral inequality and a necessary and sufficient condition on quadratic matrix inequalities reported recently. Finally, three numerical examples show that the obtained results outperform some existing ones.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:380:y:2020:i:c:s009630032030223x
    DOI: 10.1016/j.amc.2020.125254
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    References listed on IDEAS

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    1. Xiong, Lianglin & Cheng, Jun & Cao, Jinde & Liu, Zixin, 2018. "Novel inequality with application to improve the stability criterion for dynamical systems with two additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 672-688.
    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. Gao, Zhen-Man & He, Yong & Wu, Min, 2019. "Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov–Krasovskii functional," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 258-269.
    4. Zeng, Hong-Bing & Liu, Xiao-Gui & Wang, Wei, 2019. "A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 1-8.
    5. 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.
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    Cited by:

    1. 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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