skip to main content
10.1145/3318299.3318304acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicmlcConference Proceedingsconference-collections
research-article

Asymptotic Stability of Nonlinear Impulsive Stochastic Systems with Markovian Switching

Published: 22 February 2019 Publication History

Abstract

In this article, we discuss a class of stochastic partial differential systems with nonlinear impulsive and Markovian switching. Some new sufficient conditions proving asymptotic stability in p-th moment of stochastic systems are derived by employing some inequality and the fixed point technique. Some well-known results are generalized and improved.

References

[1]
Ksendal, B. 1995. Stochastic differential equations (4th ed.). Springer. New York.
[2]
Afanas'ev V. N. Kolmanovskii V. B. Nosov V. R. 1996. Stability of Stochastic Systems. In: Mathematical Theory of Control Systems Design. Mathematics and Its Applications, vol 341. Springer, Dordrecht.
[3]
Liu, K. 2006. Stability of Infinite Dimensional Stochastic Differential Equations with Applications. Chapman and Hall, CRC, London.
[4]
Mao, X. 1997. Stochastic Differential Equations and Applications. Horwood, Chichestic, UK.
[5]
Wang, B. Zhu, Q. 2017. Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems. Systems and Control Letters. 105(Jul. 2017), 55--61.
[6]
Ji, Y. Chizeck, H. J. 1990. Controllability, stability and continuous time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control. 35, 7 (Jul. 1990), 778--788.
[7]
Mariton, M. 1990. Jump linear systems in automatic control. Marcel Dekker, New York.
[8]
Basak, G. K. Bisi, A. Ghosh, M. K. 1996. Stability of a random diffusion with linear drift. Journal of Mathematics Analysis and Application.202, 2 (Sep. 1996), 604--622.
[9]
Mao, X. 1999. Stability of stochastic differential equations with Markovian switching. Stochastic Process and Application. 79, 1 (Jan. 1999), 45--67.
[10]
Li, D. Fan, X. 2017. Exponential stability of impulsive stochastic partial differential equations with delays. Statistics and Probability Letters. 126(Jul. 2017), 185--192.
[11]
Samoilenko, A. M. Perestyuk, N. A. 1995. Impulsive Differential Equations, World Scientific, Singapore.
[12]
Yang, T. 2001. Impulsive systems and control: Theory and applications. Huntington, Nova Science Publishers, NY.
[13]
Sun, J. T. Zhang, Y. P. 2003. Stability analysis of impulsive control systems. IEEE Proceedings of Control Theory and Applications. 150, 4 (Aug. 2003), 331--334.
[14]
Liu, X. Impulsive stabilization and applications to population growth models. Nonlinear Dyn. Syst. Theory. 2 (Aug. 2002), 173--184.
[15]
Wu, S. J. Han, D. Meng, X. Z. 2004. P-Moment stability of stochastic differential equations with jumps, Applied Mathematics and Computation. 152, 2 (May. 2004), 505--519.
[16]
Nieto, J. J. Rodriguez-Lopez, R. 2007. Boundary value problems for a class of impulsive functional equations, Comput. Math. Appl. 55, 12(Jun. 2008), 2715--2731.
[17]
Nieto, J. J. Rodriguez-Lopez, R. 2007. New comparison results for impulsive integro-differential equations and applications, J. Math. Anal. Appl. 328, 2 (Apr. 2007), 1343--1368.
[18]
Sakthivel, R. Luo, J. Asymptotic stability of nonlinear impulsive stochastic differential equations, Statistics and Probability Lett. 79, 9(May. 2009), 1219--1223.
[19]
Sakthivel, R. Luo, J. Asymptotic stability of impulsive stochastic partial differential equations with infinite delays, Journal of Mathematical Analysis and Applications. 356, 1 (Aug. 2009), 1--6.
[20]
Nguyen Tien, D. Neutral stochastic differential equations driven by fractional Brownian with impulsive effects and varying-time delays, Journal of the Korean Statistical Society. 43, 4 (Dec. 2014), 599--608.
[21]
Luo, J. Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays, J. Math. Anal. Appl. 342, 2 (Jun. 2008), 753--760.
[22]
Da Prato, G. Zabczyk, J. 1992. Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge.

Index Terms

  1. Asymptotic Stability of Nonlinear Impulsive Stochastic Systems with Markovian Switching

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Other conferences
    ICMLC '19: Proceedings of the 2019 11th International Conference on Machine Learning and Computing
    February 2019
    563 pages
    ISBN:9781450366007
    DOI:10.1145/3318299
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    In-Cooperation

    • Southwest Jiaotong University

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 22 February 2019

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. Markovian switching
    2. Nonlinear impulsive
    3. asymptotic stability
    4. fixed points
    5. stochastic systems

    Qualifiers

    • Research-article
    • Research
    • Refereed limited

    Funding Sources

    • the Major Project of School-Level
    • the National Natural Science Project of China

    Conference

    ICMLC '19

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • 0
      Total Citations
    • 38
      Total Downloads
    • Downloads (Last 12 months)0
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 03 Mar 2025

    Other Metrics

    Citations

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media