IDEAS home Printed from https://ideas.repec.org/a/hin/complx/6048909.html
   My bibliography  Save this article

A Generalization of the Cauchy-Schwarz Inequality and Its Application to Stability Analysis of Nonlinear Impulsive Control Systems

Author

Listed:
  • Yang Peng
  • Jiang Wu
  • Limin Zou
  • Yuming Feng
  • Zhengwen Tu

Abstract

In this paper, we first present a generalization of the Cauchy-Schwarz inequality. As an application of our result, we obtain a new sufficient condition for the stability of a class of nonlinear impulsive control systems. We end up this note with a numerical example which shows the effectiveness of our method.

Suggested Citation

  • Yang Peng & Jiang Wu & Limin Zou & Yuming Feng & Zhengwen Tu, 2019. "A Generalization of the Cauchy-Schwarz Inequality and Its Application to Stability Analysis of Nonlinear Impulsive Control Systems," Complexity, Hindawi, vol. 2019, pages 1-7, March.
    • Handle: RePEc:hin:complx:6048909
    DOI: 10.1155/2019/6048909
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/6048909.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/6048909.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/6048909?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
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Lan & Yang, Xinsong & Xu, Chen & Feng, Jianwen, 2017. "Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 22-30.
    2. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
    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. Liang, Xiyin & Qi, Guoyuan, 2017. "Mechanical analysis of Chen chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 173-177.
    2. Dong, Chengwei & Yang, Min & Jia, Lian & Li, Zirun, 2024. "Dynamics investigation and chaos-based application of a novel no-equilibrium system with coexisting hidden attractors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    3. Wu, Wen-Juan & Chen, Zeng-Qiang & Yuan, Zhu-Zhi, 2009. "A computer-assisted proof for the existence of horseshoe in a novel chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2756-2761.
    4. Megam Ngouonkadi, E.B. & Fotsin, H.B. & Louodop Fotso, P. & Kamdoum Tamba, V. & Cerdeira, Hilda A., 2016. "Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 151-163.
    5. Ghamati, Mina & Balochian, Saeed, 2015. "Design of adaptive sliding mode control for synchronization Genesio–Tesi chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 111-117.
    6. Lijuan Chen & Mingchu Yu & Jinnan Luo & Jinpeng Mi & Kaibo Shi & Song Tang, 2024. "Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity," Mathematics, MDPI, vol. 12(12), pages 1-17, June.
    7. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    9. Wang, Lingyu & Huang, Tingwen & Xiao, Qiang, 2018. "Global exponential synchronization of nonautonomous recurrent neural networks with time delays on time scales," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 263-275.
    10. Wang, Pengfei & Li, Shaoyu & Su, Huan, 2020. "Stabilization of complex-valued stochastic functional differential systems on networks via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    11. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.
    12. Wu, Yue & Zhou, Xiaobing & Chen, Jia & Hui, Bei, 2009. "Chaos synchronization of a new 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1812-1819.
    13. Gao, Wei & Yan, Li & Saeedi, Mohammadhossein & Saberi Nik, Hassan, 2018. "Ultimate bound estimation set and chaos synchronization for a financial risk system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 19-33.
    14. Faradja, Philippe & Qi, Guoyuan, 2020. "Analysis of multistability, hidden chaos and transient chaos in brushless DC motor," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    15. Wu, Jiening & Wang, Lidan & Chen, Guanrong & Duan, Shukai, 2016. "A memristive chaotic system with heart-shaped attractors and its implementation," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 20-29.
    16. Jinlong Shu & Lianglin Xiong & Tao Wu & Zixin Liu, 2019. "Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay," Mathematics, MDPI, vol. 7(1), pages 1-23, January.
    17. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2021. "Exponential synchronization of fractional-order complex chaotic systems and its application," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    18. Qi, Guoyuan & van Wyk, Michaël Antonie & van Wyk, Barend Jacobus & Chen, Guanrong, 2009. "A new hyperchaotic system and its circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2544-2549.
    19. Wu, Ranchao & Fang, Tianbao, 2015. "Stability and Hopf bifurcation of a Lorenz-like system," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 335-343.
    20. Guohui Li & Xiangyu Zhang & Hong Yang, 2019. "Numerical Analysis, Circuit Simulation, and Control Synchronization of Fractional-Order Unified Chaotic System," Mathematics, MDPI, vol. 7(11), pages 1-18, November.

    More about this item

    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:hin:complx:6048909. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.