Destabilizing effect of random parametric perturbations of the white-noise type in some quasilinear continuous and discrete dynamical systems |
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Authors: | D H Korenivs’kyi |
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Institution: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv |
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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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1719–1724, December, 2005. |
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