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ℋ ∞ ‐Norm Computation for Large and Sparse Descriptor Systems
Author(s) -
Benner Peter,
Voigt Matthias
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210383
Subject(s) - computation , norm (philosophy) , mathematics , computer science , algorithm , political science , law
In this paper we discuss the problem of computing the ℋ ∞ ‐norms of transfer functions associated to large‐scale descriptor systems. We exploit the relationship between the ℋ ∞ ‐norm and the structured complex stability radius of the corresponding system pencil. To compute the structured stability radius we consider so‐called structured pseudospectra. Namely, we have to find the pseudospectrum that touches the imaginary axis. Therefore, we set up an iteration over the real part of the rightmost pseudoeigenvalue. For that we use a new fast iterative scheme which is based on certain rank‐1 perturbations of the system pencil. Finally, we illustrate the performance of our algorithm by using a real‐world example. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)