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Ukrainian Mathematical Journal

, Volume 57, Issue 12, pp 2021–2026 | Cite as

Destabilizing effect of random parametric perturbations of the white-noise type in some quasilinear continuous and discrete dynamical systems

  • D. H. Korenivs’kyi
Article
  • 21 Downloads

Abstract

We describe the destabilizing (in the sense of a decrease in the reserve of mean-square asymptotic stability) effect of random parametric perturbations of the white-noise type in quasilinear continuous and discrete dynamical systems (Lur’e-Postnikov systems of automatic control with nonlinear feedback). We use stochastic Lyapunov functions in the form of linear combinations of the types “a quadratic form of phase coordinates plus the integral of a nonlinearity” (continuous systems) and “a quadratic form of phase coordinates plus the integral sum for a nonlinearity” (discrete systems) and the matrix algebraic Sylvester equations associated with stochastic Lyapunov functions of this form.

Keywords

Dynamical System Linear Combination Quadratic Form Automatic Control Lyapunov Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    D. G. Korenevskii, “The effect of random parametric perturbations of the white-noise type in linear discrete dynamical systems is solely destabilizing,” Dokl. Ross. Akad. Nauk, 378, No. 3, 310–313 (2001).zbMATHMathSciNetGoogle Scholar
  2. 2.
    D. H. Korenivs’kyi, “On the impossibility of stabilization of solutions of a system of linear deterministic difference equations by perturbations of its coefficients by stochastic processes of “ white-noise” type,” Ukr. Mat. Zh., 54, No. 2, 285–288 (2002).Google Scholar
  3. 3.
    D. G. Korenevskii, Stability of Dynamical Systems under Random Perturbations of Their Parameters. Algebraic Criteria [in Russian], Naukova Dumka, Kiev (1989).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • D. H. Korenivs’kyi
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyiv

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