Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy Systems
The relaxation method of Tuan <italic>et al.</italic> (2001, Theorem 2.2) has been used in various studies to deal with parameterized linear matrix inequalities (PLMIs) without excessively increasing computational complexity. Inspired by this point, this paper proposes an improved relaxa...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9819833/ |
| _version_ | 1798038354318589952 |
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| author | Sung Hyun Kim |
| author_facet | Sung Hyun Kim |
| author_sort | Sung Hyun Kim |
| collection | DOAJ |
| description | The relaxation method of Tuan <italic>et al.</italic> (2001, Theorem 2.2) has been used in various studies to deal with parameterized linear matrix inequalities (PLMIs) without excessively increasing computational complexity. Inspired by this point, this paper proposes an improved relaxation method that can further reduce the conservatism of Tuan <italic>et al.</italic> (2001, Theorem 2.2) despite no additional slack variables, as well as reduce the number of LMIs (and LMI rows). To be specific, the reduction of both conservatism and computational complexity is verified through the well-known stabilization problems of both continuous-time and discrete-time T-S fuzzy systems, which shows the potential of the proposed method for its extension to other PLMI-based stabilization conditions. |
| first_indexed | 2024-04-11T21:39:03Z |
| format | Article |
| id | doaj.art-0fbd6f71eb7e42cb81408fd2402efd19 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-11T21:39:03Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-0fbd6f71eb7e42cb81408fd2402efd192022-12-22T04:01:39ZengIEEEIEEE Access2169-35362022-01-0110718307183610.1109/ACCESS.2022.31887899819833Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy SystemsSung Hyun Kim0https://orcid.org/0000-0003-2495-7117School of Electrical Engineering, University of Ulsan, Nam-gu, Ulsan, South KoreaThe relaxation method of Tuan <italic>et al.</italic> (2001, Theorem 2.2) has been used in various studies to deal with parameterized linear matrix inequalities (PLMIs) without excessively increasing computational complexity. Inspired by this point, this paper proposes an improved relaxation method that can further reduce the conservatism of Tuan <italic>et al.</italic> (2001, Theorem 2.2) despite no additional slack variables, as well as reduce the number of LMIs (and LMI rows). To be specific, the reduction of both conservatism and computational complexity is verified through the well-known stabilization problems of both continuous-time and discrete-time T-S fuzzy systems, which shows the potential of the proposed method for its extension to other PLMI-based stabilization conditions.https://ieeexplore.ieee.org/document/9819833/Slack variable-free relaxation methodparameterized linear matrix inequalityfuzzy systemsstabilization problem |
| spellingShingle | Sung Hyun Kim Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy Systems IEEE Access Slack variable-free relaxation method parameterized linear matrix inequality fuzzy systems stabilization problem |
| title | Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy Systems |
| title_full | Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy Systems |
| title_fullStr | Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy Systems |
| title_full_unstemmed | Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy Systems |
| title_short | Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy Systems |
| title_sort | improvement of slack variable free relaxation method and its application to control design of t s fuzzy systems |
| topic | Slack variable-free relaxation method parameterized linear matrix inequality fuzzy systems stabilization problem |
| url | https://ieeexplore.ieee.org/document/9819833/ |
| work_keys_str_mv | AT sunghyunkim improvementofslackvariablefreerelaxationmethodanditsapplicationtocontroldesignoftsfuzzysystems |