Stochastic stability criteria for two-dimensional linear autonomous systems perturbed by white noise

2021/04/04 by M. M. Shumafov, Shumafov, M. M., V. B. Tlyachev +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #60H10 (Primary) 37H30 #93D30 (Secondary) #Dynamical Systems (math.DS) #Elasticity and Wave Propagation #FOS: Mathematics #FOS: Physical sciences #Mathematical Control Systems and Analysis #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations #math-ph #math.DS #math.MP #msc:37H30 #msc:60H10 #msc:93D30

paper · pdf · doi:10.48550/arxiv.2104.01637

14 pages

arxiv created 2021/04/04 · openalex publication_date 2021/04/04 · arxiv updated 2021/04/06 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28

Abstract

We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of stochastic differential equations representing the system with white noise are considered. The investigation of stochastic stability of the systems considered is based on the construction of special Lyapunov functions in the quadratic forms. The bifurcation value of the white noise intensity at which a system first becomes unstable is presented in the analytical expression. As an example a damped harmonic oscillator with randomly perturbed parameters is considered.

Citations

• The general problem of the stability of motion

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