IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v386y2020ics0096300320304781.html
   My bibliography  Save this article

pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation

Author

Listed:
  • Zhang, Huasheng
  • Zhuang, Guangming
  • Sun, Wei
  • Li, Yongmin
  • Lu, Junwei

Abstract

The problem of pth moment asymptotic interval stability and stabilization for linear stochastic systems is investigated in this paper. Firstly, we define the generalized H-representation which is very helpful to transform stochastic systems into deterministic systems. Then, the problems of pth moment interval stability, the decay rate of state response and the estimation of pth moment Lyapunov exponent are proposed with the help of the model-transformation method. Furthermore, the criteria for pth moment interval stabilization of the linear stochastic systems are addressed. Some necessary numerical examples are also provided to show the effectiveness of the addressed method.

Suggested Citation

  • Zhang, Huasheng & Zhuang, Guangming & Sun, Wei & Li, Yongmin & Lu, Junwei, 2020. "pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304781
    DOI: 10.1016/j.amc.2020.125520
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320304781
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125520?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. Xie, Jing & Kao, Yonggui & Wang, Changhong & Gao, Cunchen, 2015. "Delay-dependent robust stability of uncertain neutral-type Itoˆ stochastic systems with Markovian jumping parameters," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 576-585.
    2. Zhang, Dian & Cheng, Jun & Ki Ahn, Choon & Ni, Hongjie, 2019. "A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 191-205.
    3. Rathinasamy, A. & Narayanasamy, J., 2019. "Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 126-152.
    4. Song, Jia-Sheng & Chang, Xiao-Heng, 2020. "H∞ controller design of networked control systems with a new quantization structure," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    5. 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).
    6. Zhuang, Guangming & Xu, Shengyuan & Xia, Jianwei & Ma, Qian & Zhang, Zhengqiang, 2019. "Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 21-32.
    7. 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.
    8. 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).
    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. Yan, Zhiguo & Zhang, Min & Chang, Gaizhen & Lv, Hui & Park, Ju H., 2022. "Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Li, Yuanen & Zhang, Huasheng & Zhang, Tingting & Geng, Han, 2023. "Interval stability/stabilization and H∞ feedback control for linear impulsive stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 437(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. 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).
    2. 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).
    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. Nguyen, Ngoc Hoai An & Kim, Sung Hyun, 2021. "Asynchronous dissipative control design for semi-Markovian jump systems with uncertain probability distribution functions of sojourn-time," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    5. 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).
    6. 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).
    7. 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).
    8. Chen, Siya & Feng, Jianwen & Wang, Jingyi & Zhao, Yi, 2020. "Almost sure exponential synchronization of drive-response stochastic memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    9. Lin, Yuqian & Zhuang, Guangming & Sun, Wei & Zhao, Junsheng & Chu, Yuming, 2021. "Resilient H∞ dynamic output feedback controller design for USJSs with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    10. Arthi, G. & Suganya, K., 2021. "Controllability of higher order stochastic fractional control delay systems involving damping behavior," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    11. Suriguga, & Kao, Yonggui & Shao, Chuntao & Chen, Xiangyong, 2021. "Stability of high-order delayed Markovian jumping reaction-diffusion HNNs with uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    12. Huang, Xin & Liu, Yamin & Wang, Yang & Zhou, Jianping & Fang, Muyun & Wang, Zhen, 2020. "L2−L∞ consensus of stochastic delayed multi-agent systems with ADT switching interaction topologies," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    13. Fang, Tian & Jiao, Shiyu & Fu, Dongmei & Su, Lei, 2021. "Passivity-based synchronization for Markov switched neural networks with time delays and the inertial term," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    14. Wang, Jinling & Liang, Jinling & Zhang, Cheng-Tang & Fan, Dongmei, 2021. "Event-triggered non-fragile control for uncertain positive Roesser model with PDT switching mechanism," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    15. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    16. Sakthivel, Rathinasamy & Suveetha, V.T. & Nithya, Venkatesh & Sakthivel, Ramalingam, 2020. "Finite-time fault detection filter design for complex systems with multiple stochastic communication and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    17. 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).
    18. 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).
    19. Zhang, Zhiming & Zheng, Wei & Lam, H.K. & Wen, Shuhuan & Sun, Fuchun & Xie, Ping, 2020. "Stability analysis and output feedback control for stochastic networked systems with multiple communication delays and nonlinearities using fuzzy control technique," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    20. Tan, Jianguo & Tan, Yahua & Guo, Yongfeng & Feng, Jianfeng, 2020. "Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(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:386:y:2020:i:c:s0096300320304781. 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.