IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v417y2022ics0096300321008535.html
   My bibliography  Save this article

Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems

Author

Listed:
  • Feng, Lichao
  • Liu, Qiumei
  • Cao, Jinde
  • Zhang, Chunyan
  • Alsaadi, Fawaz

Abstract

For an unstable Markov jump stochastic differential system (MJ-SDS) with high nonlinearity, can one introduce a discrete feedback control to stabilize it? This question has been well answered for the case of the feedback control derived from discrete state observations, in the form of H∞ stabilization and exponential stabilization. Whereas, the existing theory can not tackle the non-autonomous systems and do not consider the factor of discrete mode observations, which are the motivations of this paper. Fortunately, for an unstable non-autonomous MJ-SDS, the feedback control, originated from discrete observations of system state and system mode, is well designed to stabilize it not only in the sense of exponential decay rate but also of polynomial decay rate and even general decay rate. Thereinto, the designing rule of discrete feedback control is given as well.

Suggested Citation

  • Feng, Lichao & Liu, Qiumei & Cao, Jinde & Zhang, Chunyan & Alsaadi, Fawaz, 2022. "Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    • Handle: RePEc:eee:apmaco:v:417:y:2022:i:c:s0096300321008535
    DOI: 10.1016/j.amc.2021.126771
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321008535
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126771?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. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    2. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
    3. Liu, Jiamin & Li, Zhao-Yan & Deng, Feiqi, 2021. "Asymptotic behavior analysis of Markovian switching neutral-type stochastic time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    4. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
    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. Jiang, Baoping & Wu, Zhengtian & Karimi, Hamid Reza, 2022. "A traverse algorithm approach to stochastic stability analysis of Markovian jump systems with unknown and uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 422(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. Zhang, Tian & Chen, Huabin, 2019. "The stability with a general decay of stochastic delay differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 294-307.
    2. Li, Yuyuan & Lu, Jianqiu & Kou, Chunhai & Mao, Xuerong & Pan, Jiafeng, 2018. "Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 152-161.
    3. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    4. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    5. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    6. Manley, Bruce & Niquidet, Kurt, 2010. "What is the relevance of option pricing for forest valuation in New Zealand?," Forest Policy and Economics, Elsevier, vol. 12(4), pages 299-307, April.
    7. Slanina, František, 2010. "A contribution to the systematics of stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3230-3239.
    8. Bertram During & Christian Hendricks & James Miles, 2016. "Sparse grid high-order ADI scheme for option pricing in stochastic volatility models," Papers 1611.01379, arXiv.org.
    9. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.
    10. 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).
    11. Andrey Itkin, 2023. "The ATM implied skew in the ADO-Heston model," Papers 2309.15044, arXiv.org.
    12. Minqiang Li, 2015. "Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(6), pages 582-595, June.
    13. Fu, Xiaozheng & Zhu, Quanxin & Guo, Yingxin, 2019. "Stabilization of stochastic functional differential systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 776-789.
    14. repec:uts:finphd:40 is not listed on IDEAS
    15. Emmanuel Coffie, 2022. "Numerical Method for Highly Non-linear Mean-reverting Asset Price Model with CEV-type Process," Papers 2205.00634, arXiv.org.
    16. Lorenzo Torricelli, 2012. "Valuation of asset and volatility derivatives using decoupled time-changed L\'evy processes," Papers 1210.5479, arXiv.org, revised Jan 2015.
    17. Silva-Correa, María de los Ángeles & Martínez-Marca, José Luís & Venegas-Martínez, Francisco, 2016. "Impacto del mercado de derivados en la política monetaria: un modelo de volatilidad estocástica [Impact of the Derivatives Market on Monetary Policy: A Stochastic Volatility Model]," MPRA Paper 75705, University Library of Munich, Germany.
    18. Lorenzo Torricelli, 2012. "Pricing joint claims on an asset and its realized variance under stochastic volatility models," Papers 1206.2112, arXiv.org.
    19. Erhan Bayraktar & Constantinos Kardaras & Hao Xing, 2010. "Valuation equations for stochastic volatility models," Papers 1004.3299, arXiv.org, revised Dec 2011.
    20. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    21. Peter Carr & Jian Sun, 2007. "A new approach for option pricing under stochastic volatility," Review of Derivatives Research, Springer, vol. 10(2), pages 87-150, May.

    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:417:y:2022:i:c:s0096300321008535. 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.