Let G(s)=C(sI - A)-1B+D be a given system where entries of A,B,C,D are polynomials in a parameter k. Then H∞ norm || G(s) ||∞ of G(s) is a function of k, and [9] presents an algorithm to express 1/(||G(s) ||∞)2 as a root of a bivariate polynomial, assuming feedthrough term D to be zero. This paper extends the algorithm in two ways: The first extension is the form of the function to be expressed. The extended algorithm can treat, not only H∞ norm, but also functions that appear in the celebrated KYP Lemma. The other extension is the range of the frequency. While H∞ norm considers the supremum of the maximum singular value of G(i ω) for the infinite range 0 ≤ω ≤ ∞ of ω, the extended algorithm treats the norm for the finite frequency range ω ≤ ω ≤
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Takuya KITAMOTO, "Extension of the Algorithm to Compute H∞ Norm of a Parametric System" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 8, pp. 2036-2045, August 2009, doi: 10.1587/transfun.E92.A.2036.
Abstract: Let G(s)=C(sI - A)-1B+D be a given system where entries of A,B,C,D are polynomials in a parameter k. Then H∞ norm || G(s) ||∞ of G(s) is a function of k, and [9] presents an algorithm to express 1/(||G(s) ||∞)2 as a root of a bivariate polynomial, assuming feedthrough term D to be zero. This paper extends the algorithm in two ways: The first extension is the form of the function to be expressed. The extended algorithm can treat, not only H∞ norm, but also functions that appear in the celebrated KYP Lemma. The other extension is the range of the frequency. While H∞ norm considers the supremum of the maximum singular value of G(i ω) for the infinite range 0 ≤ω ≤ ∞ of ω, the extended algorithm treats the norm for the finite frequency range ω ≤ ω ≤
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.2036/_p
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@ARTICLE{e92-a_8_2036,
author={Takuya KITAMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Extension of the Algorithm to Compute H∞ Norm of a Parametric System},
year={2009},
volume={E92-A},
number={8},
pages={2036-2045},
abstract={Let G(s)=C(sI - A)-1B+D be a given system where entries of A,B,C,D are polynomials in a parameter k. Then H∞ norm || G(s) ||∞ of G(s) is a function of k, and [9] presents an algorithm to express 1/(||G(s) ||∞)2 as a root of a bivariate polynomial, assuming feedthrough term D to be zero. This paper extends the algorithm in two ways: The first extension is the form of the function to be expressed. The extended algorithm can treat, not only H∞ norm, but also functions that appear in the celebrated KYP Lemma. The other extension is the range of the frequency. While H∞ norm considers the supremum of the maximum singular value of G(i ω) for the infinite range 0 ≤ω ≤ ∞ of ω, the extended algorithm treats the norm for the finite frequency range ω ≤ ω ≤
keywords={},
doi={10.1587/transfun.E92.A.2036},
ISSN={1745-1337},
month={August},}
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TY - JOUR
TI - Extension of the Algorithm to Compute H∞ Norm of a Parametric System
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2036
EP - 2045
AU - Takuya KITAMOTO
PY - 2009
DO - 10.1587/transfun.E92.A.2036
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2009
AB - Let G(s)=C(sI - A)-1B+D be a given system where entries of A,B,C,D are polynomials in a parameter k. Then H∞ norm || G(s) ||∞ of G(s) is a function of k, and [9] presents an algorithm to express 1/(||G(s) ||∞)2 as a root of a bivariate polynomial, assuming feedthrough term D to be zero. This paper extends the algorithm in two ways: The first extension is the form of the function to be expressed. The extended algorithm can treat, not only H∞ norm, but also functions that appear in the celebrated KYP Lemma. The other extension is the range of the frequency. While H∞ norm considers the supremum of the maximum singular value of G(i ω) for the infinite range 0 ≤ω ≤ ∞ of ω, the extended algorithm treats the norm for the finite frequency range ω ≤ ω ≤
ER -