On computing the infinity norm

Author

Robel, Greg

Author_Institution

Boeing Co., Seattle, WA, USA

Volume

34

Issue

8

fYear

1989

fDate

8/1/1989 12:00:00 AM

Firstpage

882

Lastpage

884

Abstract

An iterative algorithm is given for computing the infinity norm of the transfer matrix of a bounded, linear, time-invariant, finite-dimensional system. The procedure, which is based on the numerically stable QZ algorithm, enables the infinite norm to be computed with a guaranteed accuracy. No ad hoc procedures, such as those for selecting a suitable grid of frequencies, for example, are used. The degree of accuracy is under the direct control of the user, with each additional decimal place of accuracy requiring ≈3.3 calls to the QZ algorithm. Experience has shown the algorithm to function reliably and in reasonable time for models of order as large as 56

Keywords

iterative methods; linear systems; matrix algebra; multidimensional systems; QZ algorithm; bounded system; degree of accuracy; finite-dimensional system; infinity norm; iterative algorithm; linear system; matrix algebra; multidimensional systems; time-invariant system; transfer matrix; Eigenvalues and eigenfunctions; Frequency; H infinity control; Hilbert space; Linear approximation; Linear systems; MIMO; Matrix decomposition; Singular value decomposition; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.29433

Filename

29433