On the Partial Stability in Probability of Nonlinear Stochastic Systems
- Authors: Vorotnikov V.I.1, Martyshenko Y.G.2
-
Affiliations:
- Ural Federal University
- Gubkin Russian State University of Oil and Gas (National Research University)
- Issue: Vol 80, No 5 (2019)
- Pages: 856-866
- Section: Stochastic Systems
- URL: https://journal-vniispk.ru/0005-1179/article/view/151385
- DOI: https://doi.org/10.1134/S0005117919050059
- ID: 151385
Cite item
Abstract
A general class of the nonlinear time-varying systems of Itô stochastic differential equations is considered. Two problems on the partial stability in probability are studied as follows: 1) the stability with respect to a given part of the variables of the trivial equilibrium; 2) the stability with respect to a given part of the variables of the partial equilibrium. The stochastic Lyapunov functions-based conditions of the partial stability in probability are established. In addition to the main Lyapunov function, an auxiliary (generally speaking, vector-valued) function is introduced for correcting the domain in which the main Lyapunov function is constructed. A comparison with the well-known results on the partial stability of the systems of stochastic differential equations is given. An example that well illustrates the peculiarities of the suggested approach is described. Also a possible unified approach to analyze the partial stability of the time-invariant and time-varying systems of stochastic differential equations is discussed.
About the authors
V. I. Vorotnikov
Ural Federal University
Author for correspondence.
Email: vorotnikov-vi@rambler.ru
Russian Federation, Yekaterinburg
Yu. G. Martyshenko
Gubkin Russian State University of Oil and Gas (National Research University)
Author for correspondence.
Email: j-mart@mail.ru
Russian Federation, Moscow
Supplementary files
