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New stability criterion of uncertain systems with time-varying delay

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  • Liu, Xingwen
  • Zhang, Hongbin

Abstract

In this paper, the stability problem of uncertain systems with arbitrarily time-varying delay is considered. Based on new Lyapunov–Krasovskii functionals and novel methods to deal with uncertainties and cross-terms, stability conditions are proposed for such systems in terms of linear matrix inequalities (LMIs), which are simpler and less conservative than existing results. A numerical example is given to illustrate our theoretical result.

Suggested Citation

  • Liu, Xingwen & Zhang, Hongbin, 2005. "New stability criterion of uncertain systems with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1343-1348.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1343-1348
    DOI: 10.1016/j.chaos.2005.04.002
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    Cited by:

    1. Yan, Huaicheng & Huang, Xinhan & Zhang, Hao & Wang, Min, 2009. "Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1668-1679.
    2. Zhang, Jinhui & Shi, Peng & Qiu, Jiqing, 2008. "Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 160-167.
    3. Tian, Junkang & Xiong, Lianglin & Liu, Jianxing & Xie, Xiangjun, 2009. "Novel delay-dependent robust stability criteria for uncertain neutral systems with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1858-1866.
    4. Xiong, Lianglin & Zhong, Shouming & Tian, Junkang, 2009. "New robust stability condition for uncertain neutral systems with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1073-1079.
    5. Lien, Chang-Hua, 2007. "Non-fragile guaranteed cost control for uncertain neutral dynamic systems with time-varying delays in state and control input," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 889-899.
    6. Yan, Huaicheng & Huang, Xinhan & Wang, Min & Zhang, Hao, 2008. "New delay-dependent stability criteria of uncertain linear systems with multiple time-varying state delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 157-165.
    7. Zhong, Qishui & Bao, Jingfu & Yu, Yongbin & Liao, Xiaofeng, 2009. "Exponential stabilization for discrete Takagi–Sugeno fuzzy systems via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2123-2127.
    8. Sun, Yeong-Jeu, 2009. "On the C(R) stability of uncertain singularly perturbed systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 182-187.
    9. Liu, Duyu & Zhong, Shouming & Xiong, Lianglin, 2009. "On robust stability of uncertain neutral systems with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2332-2339.
    10. Yan, Huaicheng & Huang, Xinhan & Wang, Min & Zhang, Hao, 2007. "Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 997-1005.
    11. Xiong, Lianglin & Zhong, Shouming & Tian, Junkang, 2009. "Novel robust stability criteria of uncertain neutral systems with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 771-777.

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