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IEEE Transactions on Automatic Control
Article . 1995 . Peer-reviewed
License: IEEE Copyright
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Article
Data sources: zbMATH Open
DBLP
Article . 1995
Data sources: DBLP
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Is the Frobenius matrix norm induced?

Authors: VijaySekhar Chellaboina; Wassim M. Haddad 0001;

Is the Frobenius matrix norm induced?

Abstract

Remind that the Frobenius norm of the matrix \(A\) with the items \(A_{\mu\nu}\) is \((\sum_\mu \sum_nu|A_{\mu\nu}|^2)^{1/2}\). From the authors' abstract: ``using the notion of dual norms we show that, up to a scalar multiple, the maximum singular value is the only unitarily invariant induced norm. As a special case of this result, it follows that the Frobenius matrix norm is not induced.'' The contribution is motivated by the performance analysis of a control for its ability to reject disturbances.

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Keywords

performance analysis of a control, matrix norms, disturbance rejection, unitarily invariant induced norm, Operator-theoretic methods, \(H^\infty\)-control, Frobenius norm, maximum singular value, Applications of operator theory in systems, signals, circuits, and control theory, dual norms

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
11
Top 10%
Top 10%
Average
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