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Symmetric Positivity Preserving Balanced Truncation
Author(s) -
Grußler Christian,
Damm Tobias
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210347
Subject(s) - truncation (statistics) , realization (probability) , reduction (mathematics) , mathematics , symmetry (geometry) , order (exchange) , truncation error , mathematical optimization , pure mathematics , statistics , economics , geometry , finance
We consider positivity preserving model order reduction of SISO linear systems. Whereas well‐established model reduction methods usually do not result in a positive approximation, we show that a symmetry characterization of balanced truncation can be used to preserve positivity after performing balanced truncation. As a consequence, the method is independent of the initial realization and always returns a symmetric reduced model. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)