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dc.contributor.author
Zheng, Yang
dc.contributor.author
Furieri, Luca
dc.contributor.author
Kamgarpour, Maryam
dc.contributor.author
Li, Na
dc.date.accessioned
2022-07-19T08:44:24Z
dc.date.available
2022-03-22T05:04:03Z
dc.date.available
2022-07-19T08:44:24Z
dc.date.issued
2022-06
dc.identifier.issn
0005-1098
dc.identifier.other
10.1016/j.automatica.2022.110211
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/538304
dc.identifier.doi
10.3929/ethz-b-000538304
dc.description.abstract
It is known that the set of internally stabilizing controller Cstab is non-convex, but it admits convex characterizations using certain closed-loop maps: a classical result is the Youla parameterization, and two recent notions are the system-level parameterization (SLP) and the input–output parameterization (IOP). In this paper, we address the existence of new convex parameterizations and discuss potential tradeoffs of each parameterization in different scenarios. Our main contributions are: (1) We reveal that only four groups of stable closed-loop transfer matrices are equivalent to internal stability: one of them is used in the SLP, another one is used in the IOP, and the other two are new, leading to two new convex parameterizations of Cstab. (2) We investigate the properties of these parameterizations after imposing the finite impulse response (FIR) approximation, revealing that the IOP has the best ability of approximating Cstab given FIR constraints. (3) These four parameterizations require no a priori doubly-coprime factorization of the plant, but impose a set of equality constraints. However, these equality constraints will never be satisfied exactly in floating-point arithmetic computation and/or implementation. We prove that the IOP is numerically robust for open-loop stable plants, in the sense that small mismatches in the equality constraints do not compromise the closed-loop stability; but a direct IOP implementation will fail to stabilize open-loop unstable systems in practice. The SLP is known to enjoy numerical robustness in the state feedback case; here, we show that numerical robustness of the four-block SLP controller requires case-by-case analysis even when the plant is open-loop stable.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Internal stability
en_US
dc.subject
Youla parameterization
en_US
dc.subject
System-level synthesis
en_US
dc.subject
Convex optimization
en_US
dc.title
System-level, input–output and new parameterizations of stabilizing controllers, and their numerical computation
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2022-03-14
ethz.journal.title
Automatica
ethz.journal.volume
140
en_US
ethz.pages.start
110211
en_US
ethz.size
16 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02650 - Institut für Automatik / Automatic Control Laboratory::09578 - Kamgarpour, Maryam (ehemalig) / Kamgarpour, Maryam (former)
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02650 - Institut für Automatik / Automatic Control Laboratory::09578 - Kamgarpour, Maryam (ehemalig) / Kamgarpour, Maryam (former)
ethz.date.deposited
2022-03-22T05:04:10Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2022-07-19T08:44:32Z
ethz.rosetta.lastUpdated
2023-02-07T04:43:36Z
ethz.rosetta.versionExported
true
ethz.COinS
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