Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations

UDC 517.9 We consider the asymptotic behaviors of solutions of certain differential equations in Banach spaces. It is proved that, under certain conditions with a restriction imposed on the perturbation term, certain classes of nonautonomous infinite-dimensional evolution equations can be almost fee...

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Дата:2026
Автори: Damak, Hanen, Hammami, Mohamed Ali
Формат: Стаття
Мова:Англійська
Опубліковано: Institute of Mathematics, NAS of Ukraine 2026
Онлайн доступ:https://umj.imath.kiev.ua/index.php/umj/article/view/8393
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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author Damak, Hanen
Hammami, Mohamed Ali
Damak, Hanen
Hammami, Mohamed Ali
author_facet Damak, Hanen
Hammami, Mohamed Ali
Damak, Hanen
Hammami, Mohamed Ali
author_sort Damak, Hanen
baseUrl_str https://umj.imath.kiev.ua/index.php/umj/oai
collection OJS
datestamp_date 2026-03-21T13:38:24Z
description UDC 517.9 We consider the asymptotic behaviors of solutions of certain differential equations in Banach spaces. It is proved that, under certain conditions with a restriction imposed on the perturbation term, certain classes of nonautonomous infinite-dimensional evolution equations can be almost feedback stabilized. We use integral inequalities and Lyapunov techniques to approach this problem. Moreover, we suggest some classes of memoryless state linear and nonlinear feedback controllers. To demonstrate the validity of the main result, an example is provided.
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spelling umjimathkievua-article-83932026-03-21T13:38:24Z Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations Damak, Hanen Hammami, Mohamed Ali Damak, Hanen Hammami, Mohamed Ali Evolution operators. Feedback controller. Non-autonomous infinite-dimensional systems. Practical stabilization. Differential equations & Dynamical Systems UDC 517.9 We consider the asymptotic behaviors of solutions of certain differential equations in Banach spaces. It is proved that, under certain conditions with a restriction imposed on the perturbation term, certain classes of nonautonomous infinite-dimensional evolution equations can be almost feedback stabilized. We use integral inequalities and Lyapunov techniques to approach this problem. Moreover, we suggest some classes of memoryless state linear and nonlinear feedback controllers. To demonstrate the validity of the main result, an example is provided. УДК 517.9 Eкспоненціальна стабілізація з практичною збіжністю неавтономних нескінченновимірних еволюційних рівнянь Досліджено асимптотичну поведінку розв'язків деяких диференціальних рівнянь у банахових просторах. Показано, що за певних умов, з обмеженням на збурювальний член, деякі класи неавтономних еволюційних рівнянь у нескінченновимірних просторах можуть бути практично стабілізовані за  зворотним зв'язком. Для розв'язання цієї задачі використано інтегральні нерівності та методи функцій Ляпунова. Крім того, запропоновано деякі класи лінійних і нелінійних регуляторів зі зворотним зв'язком за станом без пам'яті. Для підтвердження основного результату наведено приклад. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8393 10.3842/umzh.v77i5.8393 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 5 (2025); 366 Український математичний журнал; Том 77 № 5 (2025); 366 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8393/10524 Copyright (c) 2025 Hanen Damak, Mohamed Ali Hammami
spellingShingle Damak, Hanen
Hammami, Mohamed Ali
Damak, Hanen
Hammami, Mohamed Ali
Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations
title Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations
title_alt Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations
title_full Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations
title_fullStr Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations
title_full_unstemmed Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations
title_short Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations
title_sort exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations
topic_facet Evolution operators. Feedback controller. Non-autonomous infinite-dimensional systems. Practical stabilization.

Dynamical Systems
url https://umj.imath.kiev.ua/index.php/umj/article/view/8393
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