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Stability analysis of Lur’e systems with additive delay components via a relaxed matrix inequality

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  • Long, Fei
  • Zhang, Chuan-Ke
  • He, Yong
  • Jiang, Lin
  • Wang, Qing-Guo
  • Wu, Min

Abstract

This paper is concerned with the stability analysis of Lur’e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov–Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.

Suggested Citation

  • Long, Fei & Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Wang, Qing-Guo & Wu, Min, 2018. "Stability analysis of Lur’e systems with additive delay components via a relaxed matrix inequality," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 224-242.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:224-242
    DOI: 10.1016/j.amc.2018.01.009
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    References listed on IDEAS

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    1. 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.
    2. Ji, Meng-Di & He, Yong & Wu, Min & Zhang, Chuan-Ke, 2015. "Further results on exponential stability of neural networks with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 175-182.
    3. F. El Haoussi & E.H. Tissir & F. Tadeo & A. Hmamed, 2011. "Delay-dependent stabilisation of systems with time-delayed state and control: application to a quadruple-tank process," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(1), pages 41-49.
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    Cited by:

    1. Li, Tao & Tang, Xiaoling & Qian, Wei & Fei, Shumin, 2019. "Hybrid-delay-dependent approach to synchronization in distributed delay neutral neural networks," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 449-463.
    2. Abolpour, Roozbeh & Khayatian, Alireza & Dehghani, Maryam & Rokhsari, Alireza, 2023. "An Equivalent Condition for Stability Analysis of LTI Systems with Bounded Time-invariant Delay," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    3. 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.

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