Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay
We obtain spectral and algebraic coefficient criteria and sufficient conditions for the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay. We consider the case of a rational correlation between delays and a “white-noise”...
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| Date: | 1998 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4856 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865792029285416960 |
|---|---|
| author | Korenevsky, D. G. Коренівський, Д. Г. |
| author_facet | Korenevsky, D. G. Коренівський, Д. Г. |
| author_institution_txt_mv | [
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"author": "Д. Г. Коренівський",
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| author_sort | Korenevsky, D. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:15:53Z |
| description | We obtain spectral and algebraic coefficient criteria and sufficient conditions for the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay. We consider the case of a rational correlation between delays and a “white-noise”-type stochastic perturbation of coefficients. We use the method of Lyapunov functions. Most results are presented in terms of the Sylvester and Lyapunov matrix algebraic equations. |
| first_indexed | 2026-03-24T03:06:30Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4856 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:06:30Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/38/a9da32353b421d36b9365d1570d98338.pdf |
| spelling | umjimathkievua-article-48562020-03-18T21:15:53Z Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay Критерии асимптотической устойчивости в среднем квадратичном решений систем линейных стохастических разностных уравнений с непрерывным временем и запаздыванием Korenevsky, D. G. Коренівський, Д. Г. We obtain spectral and algebraic coefficient criteria and sufficient conditions for the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay. We consider the case of a rational correlation between delays and a “white-noise”-type stochastic perturbation of coefficients. We use the method of Lyapunov functions. Most results are presented in terms of the Sylvester and Lyapunov matrix algebraic equations. Одержано спек гральний і алгебраїчні коефіцієнтні критерії та достатні умови асимптотичної стійкості в середньому квадратичному розв'язків вказаних у назві статті систем різницевих рівнянь. Розглянуто випадок раціонального співвідношення між запізненнями та стохастичного збурення коефіцієнтів типу „білого" шуму. Використовується метод функцій Ляпунова. Більшість результатів наведено в термінах матричних алгебраїчних рівнянь Сільвесгра і Ляпунова. Institute of Mathematics, NAS of Ukraine 1998-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4856 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 8 (1998); 1073–1081 Український математичний журнал; Том 50 № 8 (1998); 1073–1081 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4856/6411 https://umj.imath.kiev.ua/index.php/umj/article/view/4856/6412 Copyright (c) 1998 Korenevsky D. G. |
| spellingShingle | Korenevsky, D. G. Коренівський, Д. Г. Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay |
| title | Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay |
| title_alt | Критерии асимптотической устойчивости в среднем квадратичном
решений систем линейных стохастических разностных уравнений с непрерывным
временем и запаздыванием |
| title_full | Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay |
| title_fullStr | Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay |
| title_full_unstemmed | Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay |
| title_short | Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay |
| title_sort | criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4856 |
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