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

• Published in: Journal 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
• Language: English
• 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

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...