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Novel inequality with application to improve the stability criterion for dynamical systems with two additive time-varying delays

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  • Xiong, Lianglin
  • Cheng, Jun
  • Cao, Jinde
  • Liu, Zixin

Abstract

In this paper, the stability of the system with two additive time-varying delay components is studied and improved stability condition is obtained. It firstly establishes two novel integral inequalities, which are better than the same type inequalities found in the literature. Secondly, a new constructed Lyapunov functional is constructed based on the additive time-varying delays property. Following two steps to handle the Lyapunov functional, the delay-dependent stability condition is obtained which in terms of linear matrix inequalities. Finally, two numerical examples are given to verify the effectiveness of the proposed method and the superiority of the results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:672-688
    DOI: 10.1016/j.amc.2017.11.020
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    References listed on IDEAS

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    1. Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Lin, Wen-Juan & Wu, Min, 2017. "Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 102-120.
    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.
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    Cited by:

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    3. Liu, Duyu & Liu, Xinzhi & Chen, Hao & Zhong, Shouming, 2020. "A PAIM control scheme on hybrid system with its application on SIDO buck converter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
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    5. 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).
    6. Shan, Yaonan & She, Kun & Zhong, Shouming & Zhong, Qishui & Shi, Kaibo & Zhao, Can, 2018. "Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 145-168.

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