Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 149, Pages 118–128 (Mi into325)  
Construction of Lyapunov Functions for Second-Order Linear Stochastic Stationary Systems

M. M. Shumafov, V. B. Tlyachev

Adyghe State University
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Abstract: In this paper, we present a construction of Lyapunov functions for second-order linear stochastic systems with constant coefficients. Based on this construction, we state necessary and sufficient conditions of the mean-square exponential stability of two-dimensional linear stationary systems. We obtain analytical expressions for the bifurcation value of the intensity of white noise acting on the parameters of the system. As an example, we consider equations of elastic vibrations whose coefficients are perturbed by white noise.
Keywords: stability, Lyapunov function, linear stochastic differential system, Gaussian white noise process.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 250, Issue 5, Pages 835–846
DOI: https://doi.org/10.1007/s10958-020-05049-9
Bibliographic databases:
Document Type: Article
UDC: 517.925.51, 519.216.73
MSC: 93D05, 93E15
Language: Russian
Citation: M. M. Shumafov, V. B. Tlyachev, “Construction of Lyapunov Functions for Second-Order Linear Stochastic Stationary Systems”, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 149, VINITI, Moscow, 2018, 118–128; J. Math. Sci. (N. Y.), 250:5 (2020), 835–846
Citation in format AMSBIB
\Bibitem{ShuTly18}
\by M.~M.~Shumafov, V.~B.~Tlyachev
\paper Construction of Lyapunov Functions for Second-Order Linear Stochastic Stationary Systems
\inbook Proceedings of the International Conference ``Actual Problems of Applied Mathematics and Physics,'' Kabardino-Balkaria, Nalchik, May 17--21, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 149
\pages 118--128
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into325}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847731}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 250
\issue 5
\pages 835--846
\crossref{https://doi.org/10.1007/s10958-020-05049-9}
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