IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v280y2016icp140-161.html

Hybrid stabilization and synchronization of nonlinear systems with unbounded delays

Author

Listed:
  • Liu, Xinzhi
  • Stechlinski, Peter

Abstract

The stabilization of nonlinear systems with bounded and unbounded time-delays via hybrid control is studied. We investigate and identify switching rules for which stabilization can be verified a priori. When this approach is inadequate, stabilizing state-dependent switching rules are constructed. This method is based on partitioning the state-space into switching regions. Unwanted physical behavior, such as chattering and Zeno behavior, is avoided. Sufficient conditions are established using Razumikhin-like theorems. The theoretical results provide insight into how hybrid control strategies can be constructed to synchronize a class of nonlinear systems with unbounded delay. The findings are illustrated through numerical simulations.

Suggested Citation

  • Liu, Xinzhi & Stechlinski, Peter, 2016. "Hybrid stabilization and synchronization of nonlinear systems with unbounded delays," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 140-161.
    • Handle: RePEc:eee:apmaco:v:280:y:2016:i:c:p:140-161
    DOI: 10.1016/j.amc.2016.01.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316300236
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.01.023?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Li, Ping & Zhong, Shou-Ming & Cui, Jin-Zhong, 2009. "Stability analysis of linear switching systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 474-480.
    2. Li, Ping & Cao, Jinde & Wang, Zidong, 2007. "Robust impulsive synchronization of coupled delayed neural networks with uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 261-272.
    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. Shi, Lin & Yang, Huilan & Wang, Xin & Zhong, Shouming & Wang, Wenqin, 2018. "Synchronization of complex networks with asymmetric coupling via decomposing matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 180-185.
    2. 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.
    3. Zhai, Shidong & Zhou, Yuan & Li, Qingdu, 2017. "Synchronization for coupled nonlinear systems with disturbances in input and measured output," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 227-237.

    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. Ma, Mihua & Zhou, Jin & Cai, Jianping, 2014. "Impulsive practical tracking synchronization of networked uncertain Lagrangian systems without and with time-delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 116-132.
    2. Luo, Mengzhuo & Liu, Xinzhi & Zhong, Shouming & Cheng, Jun, 2018. "Synchronization of multi-stochastic-link complex networks via aperiodically intermittent control with two different switched periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 20-38.
    3. Mishra, Shalabh Kumar & Upadhyay, Dharmendra Kumar & Gupta, Maneesha, 2018. "An approach to improve the performance of fractional-order sinusoidal oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 126-135.
    4. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Synchronization in complex delayed dynamical networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 684-692.
    5. Yi, Chengbo & Feng, Jianwen & Wang, Jingyi & Xu, Chen & Zhao, Yi, 2017. "Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 78-90.
    6. Guo, Yingjia, 2017. "Stochastic regime switching SIR model driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 1-11.
    7. Lifei Chen & Yonghui Sun & Qingli Yang, 2013. "Entrained Collective Rhythms of Multicellular Systems: Partial Impulsive Control Strategy," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Global synchronization in general complex delayed dynamical networks and its applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 729-742.
    9. Feng, Xiaomei & Zhang, Fengqin & Wang, Wenjuan, 2011. "Global exponential synchronization of delayed fuzzy cellular neural networks with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 9-16.
    10. Song Zheng, 2014. "Adaptive Impulsive Observer for Outer Synchronization of Delayed Complex Dynamical Networks with Output Coupling," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    11. Waseem, Waseem & Sulaiman, M. & Aljohani, Abdulah Jeza, 2020. "Investigation of fractional models of damping material by a neuroevolutionary approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    12. Yi-You Hou, 2015. "Robust chaos synchronisation for a class of disturbed Rössler systems with multiple time-delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 1909-1916, August.
    13. Luo, Mengzhuo & Liu, Xinzhi & Zhong, Shouming & Cheng, Jun, 2018. "Synchronization of stochastic complex networks with discrete-time and distributed coupling delayed via hybrid nonlinear and impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 381-393.
    14. Gang Zhang & Yinfang Song & Xiaoyou Liu, 2024. "Exponential Synchronization of Coupled Neural Networks with Hybrid Delays and Stochastic Distributed Delayed Impulses," Mathematics, MDPI, vol. 12(13), pages 1-22, June.
    15. Yang Fang & Kang Yan & Kelin Li, 2014. "Synchronization of Chaotic Delayed Neural Networks via Impulsive Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    16. Xuehui Mei & Jiuju Xing & Haijun Jiang & Cheng Hu & Liwei Zhang, 2013. "Adaptive Synchronization for a Class of Cellular Neural Networks with Pantograph Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    17. Dong, Shiyu & Shi, Kaibo & Wen, Shiping & Shen, Yuan & Zhong, Shouming, 2023. "Almost surely synchronization of directed coupled neural networks via stochastic distributed delayed impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    18. Palanivel, J. & Suresh, K. & Sabarathinam, S. & Thamilmaran, K., 2017. "Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 33-41.
    19. Kanit Mukdasai & Akkharaphong Wongphat & Piyapong Niamsup, 2012. "Robust Exponential Stability Criteria of LPD Systems with Mixed Time‐Varying Delays and Nonlinear Perturbations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    20. Wang, Kai & Teng, Zhidong & Jiang, Haijun, 2008. "Adaptive synchronization of neural networks with time-varying delay and distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 631-642.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:280:y:2016:i:c:p:140-161. 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.