Construction of Lyapunov Functions for Second-Order Linear Stochastic Stationary Systems

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 obt...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 250; no. 5; pp. 835 - 846
Main Authors Shumafov, M. M., Tlyachev, V. B.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2020
Springer
Springer Nature B.V
Subjects
Bifurcations
Dimensional stability
Liapunov functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Noise intensity
Stability analysis
Stochastic systems
Two dimensional analysis
White noise
93D05
93E15
Gaussian white noise process
stability
linear stochastic differential system
Lyapunov function
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-05049-9