DocumentCode
1160527
Title
Is the Frobenius matrix norm induced?
Author
Chellaboina, Vijaya-Sekhar ; Haddad, Wassim M.
Author_Institution
Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
Volume
40
Issue
12
fYear
1995
fDate
12/1/1995 12:00:00 AM
Firstpage
2137
Lastpage
2139
Abstract
In this paper we answer the question of whether (or not) there exist normed input-output vector spaces that induce the Frobenius matrix norm. Specifically, 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
Keywords
closed loop systems; control system analysis computing; eigenvalues and eigenfunctions; matrix algebra; Frobenius matrix; closed loop systems; eigenvalues; feedback; induced norm; maximum singular value; normed input-output vector spaces; Aerospace engineering; Centralized control; Control systems; Extraterrestrial measurements; Feedback control; Hydrogen; Performance analysis; Steady-state; Stochastic resonance; White noise;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/9.478340
Filename
478340
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