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Delay-dependent state feedback stabilization for a networked control model with two additive input delays

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  • Shao, Hanyong
  • Zhang, Zhengqiang

Abstract

This paper is centered on delay-dependent state feedback stabilization for a networked control model with two additive input delays. Firstly delay-dependent stability is investigated. By splitting the whole delay interval into subintervals according to the delays, a Lyapunov functional is constructed. To reduce conservatism we handle the Lyapunov functional in two ways. More specifically, we take the Lyapunov functional as a whole to examine its positive definite, rather than restrict each term of it to positive definite as usual. In addition, when estimating the derivative of the Lyapunov functional, we manage to get a fairly tighter upper bound by introducing different slack variables for the different subintervals. The resulting stability results turn out dependent on the two delays separately, and less conservative than some existing ones. Then, based on the stability results state feedback stabilization is studied. Delay-dependent conditions are formulated for the controller such that the closed-loop system is asymptotically stable. Finally examples are given to show the less conservatism of the stability results and the effectiveness of the proposed stabilization method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:748-758
    DOI: 10.1016/j.amc.2015.05.114
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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.
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    Cited by:

    1. Chen, Guoliang & Xia, Jianwei & Zhuang, Guangming & Zhao, Junsheng, 2018. "Improved delay-dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 1-17.
    2. Wang, Yingchun & Zheng, Yu & Xie, Xiangpeng & Yang, Jun, 2020. "An improved reduction method based networked control against false data injection attacks and stochastic input delay," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    3. Xia, Weifeng & Xu, Shengyuan & Lu, Junwei & Li, Yongmin & Chu, Yuming & Zhang, Zhengqiang, 2021. "Event-triggered filtering for discrete-time Markovian jump systems with additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    4. Xu, Qiyi & Zhang, Yijun & He, Wangli & Xiao, Shunyuan, 2017. "Event-triggered networked H∞ control of discrete-time nonlinear singular systems," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 368-382.
    5. 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.
    6. Shao, Hanyong & Li, Huanhuan & Zhu, Chuanjie, 2017. "New stability results for delayed neural networks," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 324-334.

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