Research

A counterexample to "positive realness preserving model reduction with H-infinity norm error bounds"


Reference:

Guiver, C. and Opmeer, M. R., 2011. A counterexample to "positive realness preserving model reduction with H-infinity norm error bounds". IEEE Transactions on Circuits and Systems. Part I: Regular Papers, 58 (6), pp. 1410-1411.

Related documents:

[img]
Preview
PDF (Guiver_IEEETSCI_2011_58_6_1410.pdf) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (350kB) | Preview

    Official URL:

    http://dx.doi.org/10.1109/tcsi.2010.2097750

    Abstract

    We provide a counterexample to the H-infinity 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-infinity norm error bounds," IEEE Trans. Circuits Syst, I, Fundam. Theory Appl., vol. 42, no. 1, pp. 23-29 (1995). The proof of the error bound is based on a lemma from an earlier paper, " A tighter relative-error bound for balanced stochastic truncation," Syst. Control Lett., vol. 14, no. 4, 307-317 (1990), which we also demonstrate is false by our counterexample. The main result of this paper was already known in the literature to be false. We state a correct H-infinity 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.

    Details

    Item Type Articles
    CreatorsGuiver, C.and Opmeer, M. R.
    DOI10.1109/tcsi.2010.2097750
    Uncontrolled Keywordscontrol theory, reduced order systems
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementGuiver_IEEETSCI_2011_58_6_1410.pdf: © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    RefereedYes
    StatusPublished
    ID Code24324

    Export

    Actions (login required)

    View Item

    Document Downloads

    More statistics for this item...