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

被引：0
|
作者：
Shumafov M.M. [1 ]
Tlyachev V.B. [1 ]
机构：
[1] Adyghe State University, Maykop
来源：
Journal of Mathematical Sciences | 2020年 / 250卷 / 5期
关键词：
93D05; 93E15; Gaussian white noise process; linear stochastic differential system; Lyapunov function; stability;
D O I：
10.1007/s10958-020-05049-9
中图分类号：
学科分类号：
摘要：
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. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
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页码：835 / 846
页数：11
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