A note on the cross Gramian for non-symmetric systems. Issue 1 (1st January 2016)

• Record Type: Journal Article
• Authors: Himpe, Christian; Ohlberger, Mario
• Is Part Of: Systems science & control engineering. Volume 4:Issue 1(2016)
• Page Start: 199
• Page End: 208
• Publication Date: 2016-01-01
• Subjects: Cross Gramian -- controllability -- observability -- decentralized control -- model reduction; System theory -- Periodicals; Automatic control -- Periodicals; 003.05
• DOI: 10.1080/21642583.2016.1215273
• Languages: English
• ISSNs: 2164-2583

Abstract

ABSTRACT: 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.