Balancing Transformations for Infinite‐Dimensional Control Systems. Issue 1 (29th November 2013)

• Record Type: Journal Article
• Authors: Reis, Timo; Selig, Tilman
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 13:Issue 1(2013)
• Page Start: 465
• Page End: 466
• Publication Date: 2013-11-29
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201310225
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: In order to facilitate model reduction by balanced truncation, we introduce state space transformations that can be used to construct an ℓ2 ‐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 ℓ2 ‐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)