A counter-example to “Positive realness preserving model reduction with H-\infty norm error bounds”

Guiver, Christopher; Opmeer, Mark R.

Abstract

We provide a counter example to the H∞ error bound for the difference of a positive real transfer function and its positive real balanced truncation stated in “Positive realness preserving model reduction with H-\infty norm error bounds” IEEE Trans. Circuits Systems I Fund. Theory Appl. 42 (1995), no. 1, 23–29. The proof of the error bound is based on a lemma from an earlier paper “A tighter relative-error bound for balanced stochastic truncation.” Systems Control Lett. 14 (1990), no. 4, 307–317, which we also demonstrate is false by our counter example. The main result of this paper was already known in the literature to be false. We state a correct H-\infty error bound for the difference of a proper positive real transfer function and its positive real balanced truncation and also an error bound in the gap metric.

Citation

Guiver, C., & Opmeer, M. R. (2011). A counter-example to “Positive realness preserving model reduction with H-\infty norm error bounds”. IEEE Transactions on Circuits and Systems I: Regular Papers, 58(6), 1410-1411. https://doi.org/10.1109/tcsi.2010.2097750

• Journal Article Type: Article
• Online Publication Date: Jan 13, 2011
• Publication Date: 2011-06
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Aug 13, 2020
• Journal: IEEE Transactions on Circuits and Systems. Part I: Regular Papers
• Print ISSN: 1549-8328
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 58
• Issue: 6
• Pages: 1410-1411
• DOI: https://doi.org/10.1109/tcsi.2010.2097750
• Keywords: control theory, reduced order systems
• Public URL: http://researchrepository.napier.ac.uk/Output/2677382