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...
Verfasser: | |
---|---|
FB/Einrichtung: | FB 10: Mathematik und Informatik |
Dokumenttypen: | Artikel |
Medientypen: | Text |
Erscheinungsdatum: | 2016 |
Publikation in MIAMI: | 28.09.2016 |
Datum der letzten Änderung: | 16.06.2021 |
Angaben zur Ausgabe: | [Electronic ed.] |
Quelle: | Systems Science & Control Engineering 4 (2016) 1, 199-208 |
Schlagwörter: | Cross Gramian; controllability; observability; decentralized control; model reduction |
Fachgebiet (DDC): | 510: Mathematik |
Lizenz: | CC BY 4.0 |
Sprache: | English |
Anmerkungen: | Finanziert durch den Open-Access-Publikationsfonds 2015/2016 der Westfälischen Wilhelms-Universität Münster (WWU Münster). |
Format: | PDF-Dokument |
URN: | urn:nbn:de:hbz:6-04269619001 |
Weitere Identifikatoren: | DOI: 10.1080/21642583.2016.1215273 |
Permalink: | https://nbn-resolving.de/urn:nbn:de:hbz:6-04269619001 |
Onlinezugriff: | 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.