Skip to main content
SpringerLink
Log in

Stability of dynamic systems with aftereffect with due regard for Markov perturbations

  • Software-Hardware Systems
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

Lyapunov-Krasovskii functionals and infinitesimal operators are employed to analyze a system for asymptotic stochastic stability on the whole and asymptotic stability on the whole.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes [in Russian], Fizmatgiz, Moscow (1994).

    MATH  Google Scholar 

  2. E. B. Dynkin, Markov Processes [in Russian], Fizmatgiz, Moscow (1969).

    Google Scholar 

  3. Ya. Kats, Lyapunov Function Method in Problems of Stability and Stabilization of Random Structure Systems [in Russian], Izd. UGAPS, Ekaterinburg (1998).

    Google Scholar 

  4. A. M. Lyapunov, General Problem of the Stability of Motion [in Russian], Gostekhizdat, Moscow (1950).

    Google Scholar 

  5. M. L. Sverdan and Ye. F. Tsarkov, Stability of Stochastic Pulse Systems [in Russian], RTU, Riga (1994).

    Google Scholar 

  6. A. V. Skorokhod, Asymptotic Methods of the Theory of Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1987).

    MATH  Google Scholar 

  7. A. N. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  8. R. Z. Hasminskii, Stability of Systems of Differential Equations under Random Perturbation of Their Parameters [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  9. J. L. Dub, Probabilistic Processes [Russian translation], Izd. Inostr. Lit., Moscow (1956).

    Google Scholar 

  10. S. L. Rogol and V. K. Yasinsky, “Analysis of exponential stability of a linear stochastic oscillator under small diffusive disturbances,” Cybernetics and Systems Analysis, No. 2, 63–72 (2004).

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    V. S. Korolyuk

  2. Yu. Fed’kovich Chernovtsy National University, Chernovtsy, Ukraine

    V. I. Musurivskii & I. V. Yurchenko

Authors
  1. V. S. Korolyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Musurivskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. V. Yurchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. I. Musurivskii or I. V. Yurchenko.

Additional information

__________

Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 134–146, November–December 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korolyuk, V.S., Musurivskii, V.I. & Yurchenko, I.V. Stability of dynamic systems with aftereffect with due regard for Markov perturbations. Cybern Syst Anal 43, 876–885 (2007). https://doi.org/10.1007/s10559-007-0112-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-007-0112-0

Keywords

Search

Navigation