IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i10p2405-d1153074.html
   My bibliography  Save this article

Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion

Author

Listed:
  • Zhengqi Ma

    (School of Mathematics and Statistic, Puer University, Puer 665000, China
    School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Shoucheng Yuan

    (School of Mathematics and Statistic, Puer University, Puer 665000, China)

  • Kexin Meng

    (College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China)

  • Shuli Mei

    (College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China)

Abstract

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

Suggested Citation

  • Zhengqi Ma & Shoucheng Yuan & Kexin Meng & Shuli Mei, 2023. "Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2405-:d:1153074
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/10/2405/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/10/2405/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Haiyan Yuan, 2021. "Some Properties of Numerical Solutions for Semilinear Stochastic Delay Differential Equations Driven by G-Brownian Motion," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-26, July.
    2. Ren, Yong & He, Qian & Gu, Yuanfang & Sakthivel, R., 2018. "Mean-square stability of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 56-66.
    3. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    4. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    5. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    6. Ma, Li & Li, Yujing & Zhu, Quanxin, 2023. "Stability analysis for a class of stochastic delay nonlinear systems driven by G-Lévy Process," Statistics & Probability Letters, Elsevier, vol. 195(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. Lu, Boliang & Zhu, Quanxin, 2024. "Stability of switched neutral stochastic functional systems with different structures under high nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    2. Zhao Li & Chen Peng, 2023. "Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense," Mathematics, MDPI, vol. 11(14), pages 1-11, July.

    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. Xia, Mingli & Liu, Linna & Fang, Jianyin & Qu, Boyang, 2024. "Exponentially weighted input-to-state stability of stochastic differential systems via event-triggered impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Wenli Wang & Junyan Bao, 2024. "Existence Results for Nonlinear Impulsive System with Causal Operators," Mathematics, MDPI, vol. 12(17), pages 1-14, September.
    3. Chunsheng Wang & Xiangdong Liu & Feng Jiao & Hong Mai & Han Chen & Runpeng Lin, 2023. "Generalized Halanay Inequalities and Relative Application to Time-Delay Dynamical Systems," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
    4. Li, Jing & Zhu, Quanxin, 2023. "Event-triggered impulsive control of stochastic functional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. Haiqing Du & Xiaojing Wang & Bo Du, 2023. "Positive Periodic Solution for Pipe/Tank Flow Configurations with Friction," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
    6. Qing Yang & Xiaojing Wang & Xiwang Cheng & Bo Du & Yuxiao Zhao, 2023. "Positive Periodic Solution for Neutral-Type Integral Differential Equation Arising in Epidemic Model," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    7. Liu, Zhiguang & Zhu, Quanxin, 2023. "Ultimate boundedness of impulsive stochastic delay differential equations with delayed impulses," Statistics & Probability Letters, Elsevier, vol. 199(C).
    8. Yin, Wensheng & Cao, Jinde, 2021. "On stability of large-scale G-SDEs: A decomposition approach," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    9. Zhao Li & Chen Peng, 2023. "Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    10. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    11. Yong Tang & Lang Zhou & Jiahui Tang & Yue Rao & Hongguang Fan & Jihong Zhu, 2023. "Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    12. Chao Wang & Yinfang Song & Fengjiao Zhang & Yuxiao Zhao, 2023. "Exponential Stability of a Class of Neutral Inertial Neural Networks with Multi-Proportional Delays and Leakage Delays," Mathematics, MDPI, vol. 11(12), pages 1-14, June.
    13. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    14. Criens, David & Niemann, Lars, 2024. "A class of multidimensional nonlinear diffusions with the Feller property," Statistics & Probability Letters, Elsevier, vol. 208(C).
    15. Sergey Kashchenko, 2023. "Van der Pol Equation with a Large Feedback Delay," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    16. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    17. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
    18. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    19. Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
    20. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.

    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:gam:jmathe:v:11:y:2023:i:10:p:2405-:d:1153074. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.