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Article: The Lq/Lp Hankel Norms of Positive Systems

TitleThe Lq/Lp Hankel Norms of Positive Systems
Authors
KeywordsLq/Lₚ Hankel norm
positive system
linear programming
semidefinite programming
Issue Date2020
PublisherInstitute of Electrical and Electronics Engineers. The Journal's web site is located at https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7782633
Citation
IEEE Control Systems Letters, 2020, v. 4 n. 2, p. 462-467 How to Cite?
AbstractThis letter is concerned with the L q /L p Hankel norms of linear time-invariant positive systems, where the Hankel norms are defined as the induced norms from vector-valued L p -past inputs to vector valued L q -future outputs. The L q /L p Hankel norms are studied in detail for general (nonpositive) LTI systems, and closed-form formulas have been derived for their characterization. However, some of them unavoidably include the absolute integral of impulse responses and/or implicit functions in their characterization and hence there remain difficulties in practical computation. In this letter we show that such difficulties are circumvented for positive systems, where positivity drastically facilitates the characterization of the past input that attains the Hankel norm. We also provide linear-programming and semi definite programming-based characterizations of the L q /L p Hankel norms of positive systems, which are useful in the case where we analyze the L q /L p Hankel norms of positive systems affected by parametric uncertainties.
Persistent Identifierhttp://hdl.handle.net/10722/289734
ISSN
2023 Impact Factor: 2.4
2023 SCImago Journal Rankings: 1.597
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorEbihara, Y-
dc.contributor.authorZHU, B-
dc.contributor.authorLam, J-
dc.date.accessioned2020-10-22T08:16:42Z-
dc.date.available2020-10-22T08:16:42Z-
dc.date.issued2020-
dc.identifier.citationIEEE Control Systems Letters, 2020, v. 4 n. 2, p. 462-467-
dc.identifier.issn2475-1456-
dc.identifier.urihttp://hdl.handle.net/10722/289734-
dc.description.abstractThis letter is concerned with the L q /L p Hankel norms of linear time-invariant positive systems, where the Hankel norms are defined as the induced norms from vector-valued L p -past inputs to vector valued L q -future outputs. The L q /L p Hankel norms are studied in detail for general (nonpositive) LTI systems, and closed-form formulas have been derived for their characterization. However, some of them unavoidably include the absolute integral of impulse responses and/or implicit functions in their characterization and hence there remain difficulties in practical computation. In this letter we show that such difficulties are circumvented for positive systems, where positivity drastically facilitates the characterization of the past input that attains the Hankel norm. We also provide linear-programming and semi definite programming-based characterizations of the L q /L p Hankel norms of positive systems, which are useful in the case where we analyze the L q /L p Hankel norms of positive systems affected by parametric uncertainties.-
dc.languageeng-
dc.publisherInstitute of Electrical and Electronics Engineers. The Journal's web site is located at https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7782633-
dc.relation.ispartofIEEE Control Systems Letters-
dc.rightsIEEE Control Systems Letters. Copyright © Institute of Electrical and Electronics Engineers.-
dc.rights©20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.-
dc.subjectLq/Lₚ Hankel norm-
dc.subjectpositive system-
dc.subjectlinear programming-
dc.subjectsemidefinite programming-
dc.titleThe Lq/Lp Hankel Norms of Positive Systems-
dc.typeArticle-
dc.identifier.emailLam, J: jlam@hku.hk-
dc.identifier.authorityLam, J=rp00133-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1109/LCSYS.2019.2952622-
dc.identifier.scopuseid_2-s2.0-85075631396-
dc.identifier.hkuros316003-
dc.identifier.volume4-
dc.identifier.issue2-
dc.identifier.spage462-
dc.identifier.epage467-
dc.identifier.isiWOS:000618810600012-
dc.publisher.placeUnited States-
dc.identifier.issnl2475-1456-

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