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On the transformation formulas of the Hankel‐norm approximation
Author(s) -
Benner Peter,
Werner Steffen W. R.
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710379
Subject(s) - hankel matrix , mathematics , norm (philosophy) , matrix norm , singular value , hankel transform , transformation (genetics) , invariant (physics) , transformation matrix , lti system theory , linear system , mathematical analysis , mathematical physics , physics , eigenvalues and eigenvectors , fourier transform , biochemistry , chemistry , kinematics , classical mechanics , quantum mechanics , political science , law , gene
The Hankel‐norm approximation of a linear time‐invariant system is a method of model reduction which yields the best approximation in the Hankel semi‐norm. For the application of the method to systems with a non‐singular descriptor matrix E we generalize the transformation formulas. The resulting formulas provide additional degrees of freedom which can be used to avoid undesired numerical operations or a resulting ill‐conditioned system. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)