RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Avtomat. i Telemekh.: Year: Volume: Issue: Page: Find

 Avtomat. i Telemekh., 2019, Issue 5, Pages 86–98 (Mi at15040)

Stochastic Systems

On the partial stability in probability of nonlinear stochastic systems

V. I. Vorotnikova, Yu. G. Martyshenkob

a Ural Federal University, Yekaterinburg, Russia
b Gubkin Russian State University of Oil and Gas (National Research University), Moscow, Russia

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.

Keywords: systems of Itô, stochastic differential equations, partial stability in probability, the method of Lyapunov functions.

DOI: https://doi.org/10.1134/S0005231019050052

Full text: PDF file (634 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Automation and Remote Control, 2019, 80:5, 856–866

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: M. M. Khrustalev

Revised: 10.09.2018
Accepted: 08.11.2018

Citation: V. I. Vorotnikov, Yu. G. Martyshenko, “On the partial stability in probability of nonlinear stochastic systems”, Avtomat. i Telemekh., 2019, no. 5, 86–98; Autom. Remote Control, 80:5 (2019), 856–866

Citation in format AMSBIB
\Bibitem{VorMar19} \by V.~I.~Vorotnikov, Yu.~G.~Martyshenko \paper On the partial stability in probability of nonlinear stochastic systems \jour Avtomat. i Telemekh. \yr 2019 \issue 5 \pages 86--98 \mathnet{http://mi.mathnet.ru/at15040} \crossref{https://doi.org/10.1134/S0005231019050052} \elib{http://elibrary.ru/item.asp?id=37541640} \transl \jour Autom. Remote Control \yr 2019 \vol 80 \issue 5 \pages 856--866 \crossref{https://doi.org/10.1134/S0005117919050059} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000468031800005} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85065983443} 

• http://mi.mathnet.ru/eng/at15040
• http://mi.mathnet.ru/eng/at/y2019/i5/p86

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
•  Number of views: This page: 41 References: 2 First page: 2