IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v349y2019icp381-392.html
   My bibliography  Save this article

On uniform ultimate boundedness of linear systems with time-varying delays and peak-bounded disturbances

Author

Listed:
  • Ding, Yucai
  • Liu, Hui
  • Xu, Hui
  • Zhong, Shouming

Abstract

This paper is devoted to a problem of uniform ultimate boundedness (UUB) for a class of linear systems with interval time-varying delays and peak-bounded disturbances. By using the Lyapunov–Krasovskii functional method, a general UUB condition and an estimation of the ultimate bound on system trajectories are developed. On the basis of the above results, linear matrix inequality (LMI) conditions on UUB of the perturbed systems under consideration are derived by constructing an appropriate Lyapunov–Krasovskii functional. Meanwhile, the ultimate bound for a prescribed disturbance attenuation level is given in the form of an ellipsoidal surface. The feasibility and effectiveness of the derived results are illustrated by two numerical examples.

Suggested Citation

  • Ding, Yucai & Liu, Hui & Xu, Hui & Zhong, Shouming, 2019. "On uniform ultimate boundedness of linear systems with time-varying delays and peak-bounded disturbances," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 381-392.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:381-392
    DOI: 10.1016/j.amc.2018.12.068
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318311299
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.12.068?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. Hien, Le Van & Trinh, Hieu, 2016. "Exponential stability of time-delay systems via new weighted integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 335-344.
    2. Zhang, Dian & Cheng, Jun & Cao, Jinde & Zhang, Dan, 2019. "Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties," Applied Mathematics and Computation, Elsevier, vol. 344, pages 230-242.
    3. Wang, Jun & Shi, Kaibo & Huang, Qinzhen & Zhong, Shouming & Zhang, Dian, 2018. "Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 211-230.
    4. Zeng, Deqiang & Zhang, Ruimei & Liu, Yajuan & Zhong, Shouming, 2017. "Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 34-46.
    5. Zhang, Ruimei & Zeng, Deqiang & Zhong, Shouming & Yu, Yongbin, 2017. "Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 57-74.
    Full references (including those not matched with items on IDEAS)

    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. Luo, Mengzhuo & Cheng, Jun & Liu, Xinzhi & Zhong, Shouming, 2019. "An extended synchronization analysis for memristor-based coupled neural networks via aperiodically intermittent control," Applied Mathematics and Computation, Elsevier, vol. 344, pages 163-182.
    2. Liu, Yan & Mei, Jingling & Li, Wenxue, 2018. "Stochastic stabilization problem of complex networks without strong connectedness," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 304-315.
    3. Yao, Xueqi & Zhong, Shouming & Hu, Taotao & Cheng, Hong & Zhang, Dian, 2019. "Uniformly stable and attractive of fractional-order memristor-based neural networks with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 392-403.
    4. Zeng, Deqiang & Pu, Zhilin & Zhang, Ruimei & Zhong, Shouming & Liu, Yajuan & Wu, Guo-Cheng, 2019. "Stochastic reliable synchronization for coupled Markovian reaction–diffusion neural networks with actuator failures and generalized switching policies," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 88-106.
    5. Gao, Zifan & Zhang, Dawei & Zhu, Shuqian, 2023. "Hybrid event-triggered synchronization control of delayed chaotic neural networks against communication delay and random data loss," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Zhan, Tao & Ma, Shuping & Chen, Hao, 2019. "Impulsive stabilization of nonlinear singular switched systems with all unstable-mode subsystems," Applied Mathematics and Computation, Elsevier, vol. 344, pages 57-67.
    7. Ge, Chao & Shi, Yanpen & Park, Ju H. & Hua, Changchun, 2019. "Robust H∞ stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 500-512.
    8. Zeng, Deqiang & Zhang, Ruimei & Liu, Xinzhi & Zhong, Shouming & Shi, Kaibo, 2018. "Pinning stochastic sampled-data control for exponential synchronization of directed complex dynamical networks with sampled-data communications," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 102-118.
    9. Yang, Huilan & Wang, Xin & Shu, Lan & Zhao, Guozhu & Zhong, Shouming, 2019. "A new sampling interval fragmentation approach to synchronization of chaotic Lur’e systems," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 12-24.
    10. Tan, Manchun & Liu, Yunfeng & Xu, Desheng, 2019. "Multistability analysis of delayed quaternion-valued neural networks with nonmonotonic piecewise nonlinear activation functions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 229-255.
    11. Feng, Yuming & Yang, Xinsong & Song, Qiang & Cao, Jinde, 2018. "Synchronization of memristive neural networks with mixed delays via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 874-887.
    12. Zhao, Kaihong, 2023. "Local exponential stability of several almost periodic positive solutions for a classical controlled GA-predation ecosystem possessed distributed delays," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    13. Wang, Xin & Su, Housheng, 2019. "Consensus of hybrid multi-agent systems by event-triggered/self-triggered strategy," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 490-501.
    14. Jian, Long & Hu, Jiangping & Wang, Jun & Shi, Kaibo, 2019. "Observer-based output feedback distributed event-triggered control for linear multi-agent systems under general directed graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    15. Feng, Zongying & Shao, Hanyong & Shao, Lin, 2020. "Further results on event-triggered H∞ networked control for neural networks with stochastic cyber-attacks," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    16. Yan, Zhilian & Guo, Tong & Zhao, Anqi & Kong, Qingkai & Zhou, Jianping, 2022. "Reliable exponential H∞ filtering for a class of switched reaction-diffusion neural networks," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    17. Zhang, Xiao-Li & Li, Hong-Li & Kao, Yonggui & Zhang, Long & Jiang, Haijun, 2022. "Global Mittag-Leffler synchronization of discrete-time fractional-order neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    18. Cai, Xiao & Zhong, Shouming & Wang, Jun & Shi, Kaibo, 2020. "Robust H∞ control for uncertain delayed T-S fuzzy systems with stochastic packet dropouts," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    19. Kwon, W. & Koo, Baeyoung & Lee, S.M., 2018. "Novel Lyapunov–Krasovskii functional with delay-dependent matrix for stability of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 149-157.
    20. Sakthivel, Ramalingam & Sakthivel, Rathinasamy & Kwon, Oh-Min & Selvaraj, Palanisamy, 2021. "Disturbance rejection for singular semi-Markov jump neural networks with input saturation," Applied Mathematics and Computation, Elsevier, vol. 407(C).

    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:349:y:2019:i:c:p:381-392. 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.