Skip to main content
SpringerLink
Log in

Absolute-in-Nonlinearity-and-Delay Stability in Quadratic Mean of Stochastic Differential-Difference Systems with Poisson Switchings

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

Algebraic coefficient conditions of absolute asymptotic stability in quadratic mean of the equilibrium of a stochastic dynamic automatic control system are obtained in the present paper. A mathematical model of this system is a system of Ito-Skorokhod stochastic differential-difference delay equations with several standard Wiener processes, Poisson perturbations, and a finite number of delays.

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. M. A. Aizerman and F. R. Gantmakher, Absolute Stability of Controlled Systems [in Russian], Izd. AN SSSR, Moscow (1963).

    Google Scholar 

  2. S. Lefschetz, Stability of Nonlinear Automatic Control Systems [Russian translation], Mir, Moscow (1967).

    Google Scholar 

  3. M. R. Liberzon, “New results on absolute stability of nonstationary controlled systems,” Avtomat. Telemekh., No. 8, 29-48 (1979).

  4. A. I. Lurye, Some Nonlinear Problems of Automatic Control Theory [in Russian], Gostekhizdat, Moscow-Leningrad (1951).

    Google Scholar 

  5. A. I. Lurye and E. N. Rozenvasser, “On methods of construction of Lyapunov functions in the theory of nonlinear controlled systems,” in: Proc. of the 1st IFAC Congress, Vol. 1, Continuous Systems Theory. Special Mathematical Problems, [in Russian], Izd. AN SSSR (1961), pp. 709-717.

  6. A. P. Molchanov and E. S. Pyatnitskii, “Lyapunov functions determining necessary and sufficient conditions of absolute stability of nonlinear nonstationary control systems. I, II, III,” Avtomat. Telemekh., No. 3, 63-73, No. 4, 5-15, No. 5, 38-49 (1986).

  7. V. Rezvan, Absolute Stability of Automatic Systems [Russian translation], Nauka, Moscow (1983).

    Google Scholar 

  8. I. I. Gikhman and A. V. Skorohod, Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

  9. I. I. Gikhman and A. V. Skorohod, Stochastic Differential Equations and Their Applications [in Russian], Nauk. Dumka, Kiev (1968).

    Google Scholar 

  10. M. L. Sverdan, E. F. Tsar'kov, and V. K. Yasinskii, Stability in Stochastic Simulation of Complex Dynamic Systems [in Ukrainian], Nad Prutom, Snyatyn (1996).

  11. E. F. Tsar'kov, Random Disturbances of Functional-Differential Equations [in Russian], Zinatne, Riga (1989).

    Google Scholar 

  12. E. F. Tsar'kov and V. K. Yasinskii, Quasilinear Stochastic Functional Differential Equations [in Russian], Orientir, Riga (1992).

    Google Scholar 

  13. D. G. Korenevskii, Stability of Dynamic Systems under Random Disturbances of Their Parameters. Algebraic Criteria [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  14. F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  15. E. A. Barbashin, Introduction to Stability Theory [in Russian], Nauka, Moscow (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yu. Fed'kovych National University, Chernivtsi, Ukraine

    O. A. Yasinskaya

Authors
  1. O. A. Yasinskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yasinskaya, O.A. Absolute-in-Nonlinearity-and-Delay Stability in Quadratic Mean of Stochastic Differential-Difference Systems with Poisson Switchings. Cybernetics and Systems Analysis 36, 898–905 (2000). https://doi.org/10.1023/A:1009465528721

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009465528721

Search

Navigation