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- Publisher Website: 10.1109/TAC.2022.3198024
- Scopus: eid_2-s2.0-85136099411
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Article: Robust structural stability, stability margins, and maximum uncertainty amplification for 2D uncertain systems via structured Lyapunov functions and matrix annihilators
Title | Robust structural stability, stability margins, and maximum uncertainty amplification for 2D uncertain systems via structured Lyapunov functions and matrix annihilators |
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Authors | |
Keywords | 2D uncertain systems Eigenvalues and eigenfunctions LMI Lyapunov methods Mathematical models robust structural stability Structural engineering Symmetric matrices Uncertain systems Uncertainty |
Issue Date | 1-Jul-2023 |
Publisher | Institute of Electrical and Electronics Engineers |
Citation | IEEE Transactions on Automatic Control, 2023, v. 68, n. 7, p. 3963-3977 How to Cite? |
Abstract | This article considers two-dimensional (2-D) uncertain systems with homogeneous or mixed dynamics, and addresses the following three problems: establishing robust structural stability, computing robust structural stability margins, and determining the maximum uncertainty amplification that preserves robust structural stability. Two sufficient linear matrix inequality (LMI) conditions are proposed for establishing robust structural stability obtained by introducing an equivalent closed-loop complex system and by searching for real or complex structured Lyapunov functions and matrix annihilators parameterized by the uncertainties and auxiliary quantities. Moreover, it is shown that lower bounds of the introduced robust structural stability margins and maximum uncertainty amplification can be obtained by solving quasi-convex optimization problems under some restrictions on the sought Lyapunov functions or on the set of uncertainties. Lastly, the nonconservatism of the proposed results is analyzed, showing that the proposed LMI condition based on the use of complex Lyapunov functions is not only sufficient but also necessary under some assumptions. |
Persistent Identifier | http://hdl.handle.net/10722/329170 |
ISSN | 2023 Impact Factor: 6.2 2023 SCImago Journal Rankings: 4.501 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chesi, Graziano | - |
dc.date.accessioned | 2023-08-05T07:55:49Z | - |
dc.date.available | 2023-08-05T07:55:49Z | - |
dc.date.issued | 2023-07-01 | - |
dc.identifier.citation | IEEE Transactions on Automatic Control, 2023, v. 68, n. 7, p. 3963-3977 | - |
dc.identifier.issn | 0018-9286 | - |
dc.identifier.uri | http://hdl.handle.net/10722/329170 | - |
dc.description.abstract | <p>This article considers two-dimensional (2-D) uncertain systems with homogeneous or mixed dynamics, and addresses the following three problems: establishing robust structural stability, computing robust structural stability margins, and determining the maximum uncertainty amplification that preserves robust structural stability. Two sufficient linear matrix inequality (LMI) conditions are proposed for establishing robust structural stability obtained by introducing an equivalent closed-loop complex system and by searching for real or complex structured Lyapunov functions and matrix annihilators parameterized by the uncertainties and auxiliary quantities. Moreover, it is shown that lower bounds of the introduced robust structural stability margins and maximum uncertainty amplification can be obtained by solving quasi-convex optimization problems under some restrictions on the sought Lyapunov functions or on the set of uncertainties. Lastly, the nonconservatism of the proposed results is analyzed, showing that the proposed LMI condition based on the use of complex Lyapunov functions is not only sufficient but also necessary under some assumptions.<br></p> | - |
dc.language | eng | - |
dc.publisher | Institute of Electrical and Electronics Engineers | - |
dc.relation.ispartof | IEEE Transactions on Automatic Control | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | 2D uncertain systems | - |
dc.subject | Eigenvalues and eigenfunctions | - |
dc.subject | LMI | - |
dc.subject | Lyapunov methods | - |
dc.subject | Mathematical models | - |
dc.subject | robust structural stability | - |
dc.subject | Structural engineering | - |
dc.subject | Symmetric matrices | - |
dc.subject | Uncertain systems | - |
dc.subject | Uncertainty | - |
dc.title | Robust structural stability, stability margins, and maximum uncertainty amplification for 2D uncertain systems via structured Lyapunov functions and matrix annihilators | - |
dc.type | Article | - |
dc.identifier.doi | 10.1109/TAC.2022.3198024 | - |
dc.identifier.scopus | eid_2-s2.0-85136099411 | - |
dc.identifier.volume | 68 | - |
dc.identifier.issue | 7 | - |
dc.identifier.spage | 3963 | - |
dc.identifier.epage | 3977 | - |
dc.identifier.eissn | 1558-2523 | - |
dc.identifier.isi | WOS:001021499000009 | - |
dc.identifier.issnl | 0018-9286 | - |