Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems
UDC 517.925.51; 681.5.03 We study the problem of generalized $H_\infty$-control for a class of linear descriptor systems with nonzero initial vector. We use a generalized performance measure characterizing the weighted level of damping of external and initial disturbances. A nondegenerate tra...
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| Date: | 2026 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | Ukrainian |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8976 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513352442183680 |
|---|---|
| author | Mazko, A. Мазко, Алексей Мазко, Олексій |
| author_facet | Mazko, A. Мазко, Алексей Мазко, Олексій |
| author_sort | Mazko, A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-22T13:31:23Z |
| description |
UDC 517.925.51; 681.5.03
We study the problem of generalized $H_\infty$-control for a class of linear descriptor systems with nonzero initial vector. We use a generalized performance measure characterizing the weighted level of damping of external and initial disturbances. A nondegenerate transformation of the system is proposed, which allows us to apply well-known methods for the evaluation and attainment of the desired performance criteria for conventional lower-order systems. A numerical example of a controlled hydraulic system with three tanks is presented. |
| doi_str_mv | 10.3842/umzh.v77i5.8976 |
| first_indexed | 2026-03-24T03:43:19Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8976 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:43:19Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b3/e5e9ef4d63f5742de94143d9ccaef0b3 |
| spelling | umjimathkievua-article-89762026-03-22T13:31:23Z Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems Еквівалентне перетворення і зважена $H_\infty$-оптимізація лінійних дескрипторних систем Mazko, A. Мазко, Алексей Мазко, Олексій Descriptor system; exogenous disturbances; H∞ control; weighted performance measure; LMI. Дескрипторна система; екзогеннi збурення; H∞-керування; зважений критерiй якостi; ЛМН. UDC 517.925.51; 681.5.03 We study the problem of generalized $H_\infty$-control for a class of linear descriptor systems with nonzero initial vector. We use a generalized performance measure characterizing the weighted level of damping of external and initial disturbances. A nondegenerate transformation of the system is proposed, which allows us to apply well-known methods for the evaluation and attainment of the desired performance criteria for conventional lower-order systems. A numerical example of a controlled hydraulic system with three tanks is presented. УДК 517.925.51; 681.5.03 Досліджується проблема узагальненого $H_\infty$-керування для класу лінійних дескрипторних систем із ненульовим початковим вектором. При цьому використано узагальнений критерій якості, що характеризує зважений рівень гасіння зовнішніх і початкових збурень. Запропоновано невироджене перетворення системи, яке дозволяє застосовувати відомі методи оцінки та досягати бажаних критеріїв якості для звичайних систем меншого порядку. Наведено числовий приклад керованої гідравлічної системи з трьома резервуарами. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8976 10.3842/umzh.v77i5.8976 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 5 (2025); 324–337 Український математичний журнал; Том 77 № 5 (2025); 324–337 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/8976/10532 Copyright (c) 2025 Олексій Мазко |
| spellingShingle | Mazko, A. Мазко, Алексей Мазко, Олексій Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems |
| title | Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems |
| title_alt | Еквівалентне перетворення і зважена $H_\infty$-оптимізація лінійних дескрипторних систем |
| title_full | Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems |
| title_fullStr | Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems |
| title_full_unstemmed | Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems |
| title_short | Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems |
| title_sort | equivalent transformation and weighted $h_\infty$-optimization of linear descriptor systems |
| topic_facet | Descriptor system exogenous disturbances H∞ control weighted performance measure LMI. Дескрипторна система екзогеннi збурення H∞-керування зважений критерiй якостi ЛМН. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8976 |
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