Analysis of Second-Order Modes of Linear Continuous-Time Systems under Positive-Real Transformations
Summary :
This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.2 pp.575-583
- Publication Date
- 2008/02/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e91-a.2.575
- Type of Manuscript
- PAPER
- Category
- Systems and Control
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Keyword
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Shunsuke KOSHITA, Yousuke MIZUKAMI, Taketo KONNO, Masahide ABE, Masayuki KAWAMATA, "Analysis of Second-Order Modes of Linear Continuous-Time Systems under Positive-Real Transformations" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 2, pp. 575-583, February 2008, doi: 10.1093/ietfec/e91-a.2.575.
Abstract: This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.2.575/_p
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@ARTICLE{e91-a_2_575,
author={Shunsuke KOSHITA, Yousuke MIZUKAMI, Taketo KONNO, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Analysis of Second-Order Modes of Linear Continuous-Time Systems under Positive-Real Transformations},
year={2008},
volume={E91-A},
number={2},
pages={575-583},
abstract={This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.},
keywords={},
doi={10.1093/ietfec/e91-a.2.575},
ISSN={1745-1337},
month={February},}
Copy
TY - JOUR
TI - Analysis of Second-Order Modes of Linear Continuous-Time Systems under Positive-Real Transformations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 575
EP - 583
AU - Shunsuke KOSHITA
AU - Yousuke MIZUKAMI
AU - Taketo KONNO
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2008
DO - 10.1093/ietfec/e91-a.2.575
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2008
AB - This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.
ER -
English
