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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 149, Pages 118–128
(Mi into325)
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Construction of Lyapunov Functions for Second-Order Linear Stochastic Stationary Systems
M. M. Shumafov, V. B. Tlyachev Adyghe State University
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.
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
Linking options:
https://www.mathnet.ru/eng/into325 https://www.mathnet.ru/eng/into/v149/p118
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Statistics & downloads: |
Abstract page: | 180 | Full-text PDF : | 347 | References: | 13 | First page: | 10 |
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