On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type
We consider the problem of mean-square stabilization of solutions of a system of linear deterministic difference equations with discrete time by perturbations of its coefficients by a stochastic “white-noise” process. The answer is negative and is based on the analysis of the corresponding matrix al...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4064 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510194992152576 |
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| author | Korenevsky, D. G. Коренівський, Д. Г. |
| author_facet | Korenevsky, D. G. Коренівський, Д. Г. |
| author_sort | Korenevsky, D. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:20:24Z |
| description | We consider the problem of mean-square stabilization of solutions of a system of linear deterministic difference equations with discrete time by perturbations of its coefficients by a stochastic “white-noise” process. The answer is negative and is based on the analysis of the corresponding matrix algebraic Sylvester equation introduced earlier by the author in the theory of stability of stochastic systems. At the same time, we answer the same question for a vector matrix system of linear difference equations with continuous time and for a vector matrix system of differential equations. |
| first_indexed | 2026-03-24T02:53:08Z |
| format | Article |
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| id | umjimathkievua-article-4064 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:53:08Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/7d/ee59d7de4199be9058e8bbb68d816b7d.pdf |
| spelling | umjimathkievua-article-40642020-03-18T20:20:24Z On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type Про неможливість стабілізації розв'язків системи лінійних детермінованих різницевих рівнянь збуреннями її коефіцієнтів стохастичними процесами типу „білого шуму" Korenevsky, D. G. Коренівський, Д. Г. We consider the problem of mean-square stabilization of solutions of a system of linear deterministic difference equations with discrete time by perturbations of its coefficients by a stochastic “white-noise” process. The answer is negative and is based on the analysis of the corresponding matrix algebraic Sylvester equation introduced earlier by the author in the theory of stability of stochastic systems. At the same time, we answer the same question for a vector matrix system of linear difference equations with continuous time and for a vector matrix system of differential equations. Ставиться питання про стабілізацію в середньому квадратичному розв'язків системи лінійних детермінованих різницевих рівнянь з дискретним часом .збуреннями її коефіцієнтів стохастич-ним процесом типу „білого шуму". Відповідь — нега тивна і ґрунтується на аналізі відповідного матричного алгебраїчного рівняння Сільвестра, введеного автором в теорію стійкості стохастичних систем раніше. Водночас дається аналогічна відповідь на таке саме питання відносно векторно-матричиої системи лінійних різницевих рівнянь з неперервним часом та векторно-матричної системи диференціальних рівнянь. Institute of Mathematics, NAS of Ukraine 2002-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4064 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 2 (2002); 285-288 Український математичний журнал; Том 54 № 2 (2002); 285-288 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4064/4838 https://umj.imath.kiev.ua/index.php/umj/article/view/4064/4839 Copyright (c) 2002 Korenevsky D. G. |
| spellingShingle | Korenevsky, D. G. Коренівський, Д. Г. On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type |
| title | On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type |
| title_alt | Про неможливість стабілізації розв'язків системи лінійних детермінованих різницевих рівнянь збуреннями її коефіцієнтів стохастичними процесами типу „білого шуму" |
| title_full | On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type |
| title_fullStr | On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type |
| title_full_unstemmed | On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type |
| title_short | On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type |
| title_sort | on the impossibility of stabilization of solutions of a system of linear deterministic difference equations by perturbations of its coefficients by stochastic processes of “white-noise” type |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4064 |
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