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

  • Type:

    Article

  • Date:

    13 January 2011

  • Publication Status:

    Published

  • Publisher

    IEEE

  • DOI:

    10.1109/tcsi.2010.2097750

  • ISSN:

    1549-8328

  • Funders:

    Historic Funder (pre-Worktribe)

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

Authors

Keywords

control theory, reduced order systems

Monthly Views:

Available Documents