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A unified framework for asymptotic and transient behavior of linear stochastic systems

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  • Yan, Zhiguo
  • Park, Ju H.
  • Zhang, Weihai

Abstract

This paper is concerned with a unified framework for asymptotic and transient behavior of stochastic systems. In order to explain this problem explicitly, a concept of mean square (γ, α)-stability is first introduced and two stability criteria are derived. By utilizing an auxiliary definition of mean square (γ, T)-stability, the relations among mean square (γ, α)-stability, mean square (γ, T)-stability and finite-time stochastic stability are established. Subsequently, two new sufficient conditions for the existence of state and output feedback mean square (γ, α)-stabilization controllers are presented in terms of matrix inequalities. A numerical algorithm is given to obtain the relation between γmin and α. Finally, an example is given to illustrate our results.

Suggested Citation

  • Yan, Zhiguo & Park, Ju H. & Zhang, Weihai, 2018. "A unified framework for asymptotic and transient behavior of linear stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 31-40.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:31-40
    DOI: 10.1016/j.amc.2017.12.023
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    References listed on IDEAS

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    1. Lembke B., 1918. "√ a. p," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 111(1), pages 709-712, February.
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    Cited by:

    1. Hu, Jun & Zhang, Panpan & Kao, Yonggui & Liu, Hongjian & Chen, Dongyan, 2019. "Sliding mode control for Markovian jump repeated scalar nonlinear systems with packet dropouts: The uncertain occurrence probabilities case," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    2. Guo, Ying & Zhao, Wei & Ding, Xiaohua, 2019. "Input-to-state stability for stochastic multi-group models with multi-dispersal and time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 114-127.
    3. Jiao, Ticao & Zong, Guangdeng & Pang, Guochen & Zhang, Housheng & Jiang, Jishun, 2020. "Admissibility analysis of stochastic singular systems with Poisson switching," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Song, Bo & Zhang, Ya & Park, Ju H., 2021. "H∞ control for Poisson-driven stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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