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Balancing Transformations for Infinite‐Dimensional Control Systems
Author(s) -
Reis Timo,
Selig Tilman
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310225
Subject(s) - realization (probability) , minimal realization , operator (biology) , mathematics , reduction (mathematics) , construct (python library) , truncation (statistics) , state space , state (computer science) , computer science , algebra over a field , control theory (sociology) , control (management) , linear system , pure mathematics , algorithm , mathematical analysis , geometry , biochemistry , statistics , chemistry , repressor , artificial intelligence , transcription factor , gene , programming language
In order to facilitate model reduction by balanced truncation, we introduce state space transformations that can be used to construct an ℓ 2 ‐balanced realization of a regular, linear input‐ouput map with nuclear Hankel‐operator directly from the system generators of an arbitrary, given realization. These balancing transformations are based on factors of the Gramians and, for infinite‐dimensional systems, they are usually unbounded operators. Subsequently the ℓ 2 ‐balanced realization can be truncated in a non‐trivial way to obtain an approximating, finite‐dimensional model. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)