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Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality

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  • Sun, Yonghui
  • Li, Ning
  • Shen, Mouquan
  • Wei, Zhinong
  • Sun, Guoqiang

Abstract

This paper is concerned with the robust H∞ control problem of uncertain linear system with interval time-varying delays. Firstly, by using Wirtinger inequality approach, after constructing a new Lyapunov functional, the novel robust delay-dependent stability and stabilization criteria are developed. These improved results are expected to have less conservatism, due to the utilization of Wirtinger inequality and consideration of the information of the lower bound of time delay. Secondly, based on the obtained criteria, the memoryless H∞ state feedback controller design scheme is presented, thus robust H∞ controller design and performance analysis for uncertain linear system are developed. For a prescribed H∞ performance level, the designed robust H∞ controller can guarantee the uncertain linear system to be robustly stable and endure a larger delay. At last, numerical examples are provided to illustrate the effectiveness and superiority of the developed results.

Suggested Citation

  • Sun, Yonghui & Li, Ning & Shen, Mouquan & Wei, Zhinong & Sun, Guoqiang, 2018. "Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 1-11.
    • Handle: RePEc:eee:apmaco:v:335:y:2018:i:c:p:1-11
    DOI: 10.1016/j.amc.2018.04.027
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    References listed on IDEAS

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    1. Liu, Xin-Ge & Wu, Min & Martin, Ralph & Tang, Mei-Lan, 2007. "Delay-dependent stability analysis for uncertain neutral systems with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(1), pages 15-27.
    2. Shao, Hanyong & Zhang, Zhengqiang, 2015. "Delay-dependent state feedback stabilization for a networked control model with two additive input delays," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 748-758.
    3. Hien, Le Van & Trinh, Hieu, 2016. "Exponential stability of time-delay systems via new weighted integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 335-344.
    4. 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.
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    Cited by:

    1. 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).

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