IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v416y2022ics009630032100833x.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032100833X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126751?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. 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).
    3. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chang, Xu-Kang & He, Yong, 2024. "Reachable set estimation of delayed Markovian jump neural networks via variables-augmented-based free-weighting-matrices method," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    2. Zhang, Ziwei & Chen, Zongjie & Sheng, Zhang & Li, Dan & Wang, Jing, 2022. "Static output feedback secure synchronization control for Markov jump neural networks under hybrid cyber-attacks," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. Guo, Fang & Luo, Mengzhuo & Cheng, Jun & Katib, Iyad & Shi, Kaibo, 2023. "Nonfragile observer-based event-triggered fuzzy tracking control for fast-sampling singularly perturbed systems with dual-layer switching mechanism and cyber-attacks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chang, Xu-Kang & He, Yong, 2024. "Reachable set estimation of delayed Markovian jump neural networks via variables-augmented-based free-weighting-matrices method," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    2. 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).
    3. Liu, Yu-An & Tang, Shengdao & Liu, Yufan & Kong, Qingkai & Wang, Jing, 2021. "Extended dissipative sliding mode control for nonlinear networked control systems via event-triggered mechanism with random uncertain measurement," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. Wu, Tianyu & Huang, Xia & Chen, Xiangyong & Wang, Jing, 2020. "Sampled-data H∞ exponential synchronization for delayed semi-Markov jump CDNs: A looped-functional approach," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    5. Jiao, Ticao & Zong, Guangdeng & Pang, Guochen & Zhang, Housheng & Jiang, Jishun, 2020. "Admissibility analysis of stochastic singular systems with Poisson switching," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    6. Han, Xin-Xin & Wu, Kai-Ning & Ding, Xiaohua, 2020. "Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    7. Wang, Dongji & Chen, Fei & Meng, Bo & Hu, Xingliu & Wang, Jing, 2021. "Event-based secure H∞ load frequency control for delayed power systems subject to deception attacks," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    8. Yang, Tianqing & Zou, Runmin & Liu, Fang & Liu, Cai & Sidorov, Denis, 2023. "Improved stabilization condition of delayed T-S fuzzy systems via an extended quadratic function negative-determination lemma," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    9. Kwon, O.M. & Lee, S.H. & Park, M.J. & Lee, S.M., 2020. "Augmented zero equality approach to stability for linear systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    10. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
    11. Xu, Qiyi & Zhang, Ning & Qi, Wenhai, 2023. "Finite-time control for discrete-time nonlinear Markov switching LPV systems with DoS attacks," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    12. Xu, Bo & Liang, Yanjun & Li, Yuan-Xin & Hou, Zhongsheng, 2022. "Adaptive command filtered fixed-time control of nonlinear systems with input quantization," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    13. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Cao, Jinde & Alsaedi, Ahmed, 2020. "Extended feedback and simulation strategies for a delayed fractional-order control system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    14. Dai, Mingcheng & Huang, Zhengguo & Xia, Jianwei & Meng, Bo & Wang, Jian & Shen, Hao, 2019. "Non-fragile extended dissipativity-based state feedback control for 2-D Markov jump delayed systems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    15. Shuoting Wang & Kaibo Shi & Jin Yang, 2022. "Improved Stability Criteria for Delayed Neural Networks via a Relaxed Delay-Product-Type Lapunov–Krasovskii Functional," Mathematics, MDPI, vol. 10(15), pages 1-14, August.
    16. Xia, Yude & Wang, Jing & Meng, Bo & Chen, Xiangyong, 2020. "Further results on fuzzy sampled-data stabilization of chaotic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    17. Yang, Chengyu & Li, Fei & Kong, Qingkai & Chen, Xiangyong & Wang, Jian, 2021. "Asynchronous fault-tolerant control for stochastic jumping singularly perturbed systems: An H∞ sliding mode control scheme," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    18. Li, Qiang & Liang, Jinling, 2022. "Non-fragile asynchronous state estimation for Markovian switching CVNs with partly accessible mode detection: The discrete-time case," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    19. Yang, Liu & Ma, Weijun & Wang, Xin, 2024. "Lagrange stability and passivity in the mean square sense of discrete-time stochastic Markovian switched neural networks with time-varying mixed delays," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    20. Jiao, Ticao & Park, Ju H. & Zong, Guangdeng & Liu, Jian & Chen, Yu, 2019. "Stochastic stability analysis of switched genetic regulatory networks without stable subsystems," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 261-277.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:416:y:2022:i:c:s009630032100833x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.