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Further refinements in stability conditions for time-varying delay systems

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  • de Oliveira, Fúlvia S.S.
  • Souza, Fernando O.

Abstract

This paper addresses the problem of assessing the stability of linear time-invariant (LTI) systems with time-varying delay. The first contribution is a new stability criterion specified as a negativity condition for a quadratic function parameterized by the delay. This result mainly follows from an augmented affine parameter-dependent Lyapunov-Krasovskii functional, which, in turn, takes advantages of convexity properties. Then, as a second contribution, we invoke a result from robust control literature to show how the proposed stability condition can be checked exactly in terms of linear matrix inequality (LMI) conditions. The improvements obtained by the proposed refinements are illustrated via numerical examples drawn from the literature.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308586
    DOI: 10.1016/j.amc.2019.124866
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    6. Liang, Xingyue & Xia, Jianwei & Chen, Guoliang & Zhang, Huasheng & Wang, Zhen, 2019. "Dissipativity-based sampled-data control for fuzzy Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 552-564.
    7. 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.
    8. Ge, Chao & Shi, Yanpen & Park, Ju H. & Hua, Changchun, 2019. "Robust H∞ stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 500-512.
    9. Li, Rongchang & Zhang, Qingling, 2018. "Robust H∞ sliding mode observer design for a class of Takagi–Sugeno fuzzy descriptor systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 158-178.
    10. 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.
    11. 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.
    12. Yang, Yuxia & Lin, Chong & Chen, Bing & Wang, Qing-Guo, 2018. "Reduced-order observer design for a class of generalized Lipschitz nonlinear systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 267-280.
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    Cited by:

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    2. Liming Ding & Liqin Chen & Dajiang He & Weiwei Xiang, 2022. "New Delay-Partitioning LK-Functional for Stability Analysis with Neutral Type Systems," Mathematics, MDPI, vol. 10(21), pages 1-13, November.
    3. 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).
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    5. Can Zhao & Kaibo Shi & Yiqian Tang & Shouming Zhong, 2022. "A New Slack Lyapunov Functional for Dynamical System with Time Delay," Mathematics, MDPI, vol. 10(23), pages 1-11, November.
    6. Wenxi Feng & Yanshan Xie & Fei Luo & Xianyong Zhang & Wenyong Duan, 2021. "Enhanced Stability Criteria of Network-Based Load Frequency Control of Power Systems with Time-Varying Delays," Energies, MDPI, vol. 14(18), pages 1-22, September.
    7. Lee, Tae H. & Park, Myeong Jin & Park, Ju H., 2021. "An improved stability criterion of neural networks with time-varying delays in the form of quadratic function using novel geometry-based conditions," Applied Mathematics and Computation, Elsevier, vol. 404(C).

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