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
fDate :
12/1/1995 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
