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Reachable set estimation for continuous delayed singularly perturbed systems with bounded disturbances

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  • Liu, Guobao
  • Chen, Xiangyong
  • Shen, Zhongyu
  • Liu, Yajuan
  • Jia, Xianglei

Abstract

Reachable set estimation problem in allusion to continuous-time singularly perturbed systems that take on time-varying delays and bounded disturbances is discussed in this paper. In many singularly perturbed systems, since the perturbed parameter κ is not available, our task is to determine an ellipsoid as small as possible which can be independent on κ. In this case, for any admissible singularly perturbed parameters, this ellipsoid can surround the states of the system. First, in order to obtain more accurate result, the delay is unequally divided into two sub-intervals and a κ-dependent Lyapunov-Krasocskii functional is established. Then, with the aid of reciprocally convex inequality for each sub-interval, sufficient delay-dependent conditions are established which can make the system states contained by a κ-independent ellipsoid. Finally, a numerical example is given to verify the validity of the result.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:416:y:2022:i:c:s009630032100833x
    DOI: 10.1016/j.amc.2021.126751
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    References listed on IDEAS

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    1. Lee, Tae H. & Park, Myeong Jin & Park, Ju H., 2021. "An improved stability criterion of neural networks with time-varying delays in the form of quadratic function using novel geometry-based conditions," Applied Mathematics and Computation, Elsevier, vol. 404(C).
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    3. 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).
    4. 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).
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    Cited by:

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    3. Liao, Wei & Liang, Taotao & Wang, Chen & Yang, Dayong, 2023. "A dimensionality reduction method for computing reachable tubes based on piecewise pseudo-time dependent Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 441(C).

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