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Improved results on reachable set estimation of singular systems

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  • Zhang, Liang
  • Feng, Zhiguang
  • Jiang, Zhengyi
  • Zhao, Ning
  • Yang, Yang

Abstract

This paper investigates the problem of reachable set estimation for a general class of continuous-time singular linear systems with time-varying delay. By employing a new Lyapunov functional candidate, a criterion with the help of linear matrix inequalities (LMIs) is developed utilizing the new inequality scaling method, free-weighting matrix and the time-delay segmentation method. The reachable set of the underlying system is bounded by the intersection of ellipsoids. The effectiveness of our results are demonstrated by the examples.

Suggested Citation

  • Zhang, Liang & Feng, Zhiguang & Jiang, Zhengyi & Zhao, Ning & Yang, Yang, 2020. "Improved results on reachable set estimation of singular systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    • Handle: RePEc:eee:apmaco:v:385:y:2020:i:c:s0096300320303805
    DOI: 10.1016/j.amc.2020.125419
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    References listed on IDEAS

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    1. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Zhen & Wang, Jian, 2020. "Reachable set estimation for Markov jump LPV systems with time delays," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    2. Xiong, Jun & Chang, Xiao-Heng & Yi, Xiaojian, 2018. "Design of robust nonfragile fault detection filter for uncertain dynamic systems with quantization," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 774-788.
    3. C. Durieu & É. Walter & B. Polyak, 2001. "Multi-Input Multi-Output Ellipsoidal State Bounding," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 273-303, November.
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    Citations

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    Cited by:

    1. Feng, Zhiguang & Zhang, Xinyue & Lam, James & Fan, Chenchen, 2023. "Estimation of reachable set for switched singular systems with time-varying delay and state jump," Applied Mathematics and Computation, Elsevier, vol. 456(C).
    2. Liao, Wei & Liang, Taotao & Wei, Xiaohui & Yin, Qiaozhi, 2022. "Probabilistic reach-Avoid problems in nondeterministic systems with time-Varying targets and obstacles," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Feng, Bo & Feng, Zhiguang & Li, Peng, 2023. "Improved results on reachable set synthesis of Markovian jump systems with time-varying delays: General asynchronous control approaches," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    4. Liu, Guobao & Chen, Xiangyong & Shen, Zhongyu & Liu, Yajuan & Jia, Xianglei, 2022. "Reachable set estimation for continuous delayed singularly perturbed systems with bounded disturbances," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    5. Chen, Ruihan & Guo, Moxuan & Zhu, Song & Qi, Yongqiang & Wang, Min & Hu, Junhao, 2022. "Reachable set bounding for linear systems with mixed delays and state constraints," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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