DocumentCode :
1423804
Title :
A Counterexample to “ Positive Realness Preserving Model Reduction With 
Norm Error Bounds”
Author :
Guiver, Chris ; Opmeer, Mark R.
Author_Institution :
Dept. of Math. Sci., Univ. of Bath, Bath, UK
Volume :
58
Issue :
6
fYear :
2011
fDate :
6/1/2011 12:00:00 AM
Firstpage :
1410
Lastpage :
1411
Abstract :
We provide a counterexample 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∞ 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∞ 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.
Keywords :
H∞ control; error statistics; stochastic processes; transfer functions; H infinity norm error bound; balanced stochastic truncation; gap metric; positive real balanced truncation; positive real transfer function; positive realness preserving model reduction; relative-error bound; Approximation methods; Equations; Mathematical model; Measurement; Reduced order systems; Stochastic processes; Transfer functions; Control theory; reduced order systems;
fLanguage :
English
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
Publisher :
ieee
ISSN :
1549-8328
Type :
jour
DOI :
10.1109/TCSI.2010.2097750
Filename :
5685595
Link To Document :
