A note on the cross Gramian for non-symmetric systems

The cross Gramian matrix is a tool for model reduction and system identification, but it is only applicable to square control systems. For symmetric systems, the cross Gramian possesses a useful relation to the system's associated Hankel singular values. Yet, many real-life models are neither s...

Authors: Himpe, Christian
Ohlberger, Mario
Division/Institute:FB 10: Mathematik und Informatik
Document types:Article
Media types:Text
Publication date:2016
Date of publication on miami:28.09.2016
Modification date:16.04.2019
Edition statement:[Electronic ed.]
Source:Systems Science & Control Engineering 4 (2016) 1, 199-208
Subjects:Cross Gramian; controllability; observability; decentralized control; model reduction
DDC Subject:510: Mathematik
License:CC BY 4.0
Language:English
Notes:Finanziert durch den Open-Access-Publikationsfonds 2015/2016 der Westfälischen Wilhelms-Universität Münster (WWU Münster).
Format:PDF document
URN:urn:nbn:de:hbz:6-04269619001
Permalink:http://nbn-resolving.de/urn:nbn:de:hbz:6-04269619001
Other Identifiers:DOI: 10.1080/21642583.2016.1215273
Digital documents:A%20note%20on%20the%20cross%20Gramian%20for%20non%20symmetric%20systems.pdf

The cross Gramian matrix is a tool for model reduction and system identification, but it is only applicable to square control systems. For symmetric systems, the cross Gramian possesses a useful relation to the system's associated Hankel singular values. Yet, many real-life models are neither square nor symmetric. In this work, concepts from decentralized control are used to approximate a cross Gramian for non-symmetric and non-square systems. To illustrate this new non-symmetric cross Gramian, it is applied in the context of model order reduction.