Invariance of Second-Order Modes of Linear Continuous-Time Systems under Typical Frequency Transformations

Masayuki KAWAMATA; Yousuke MIZUKAMI; Shunsuke KOSHITA

doi:10.1093/ietfec/e90-a.7.1481

Invariance of Second-Order Modes of Linear Continuous-Time Systems under Typical Frequency Transformations

Masayuki KAWAMATA, Yousuke MIZUKAMI, Shunsuke KOSHITA

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This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpass-highpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This means that any transformed system that is generated from a prototype system has the same second-order modes as those of the prototype system. We achieve the derivation of this result by describing the state-space equations and the controllability/observability Gramians of transformed systems.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.7 pp.1481-1486

Publication Date: 2007/07/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e90-a.7.1481

Type of Manuscript: LETTER

Category: Systems and Control

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Masayuki KAWAMATA, Yousuke MIZUKAMI, Shunsuke KOSHITA, "Invariance of Second-Order Modes of Linear Continuous-Time Systems under Typical Frequency Transformations" in IEICE TRANSACTIONS on Fundamentals, vol. E90-A, no. 7, pp. 1481-1486, July 2007, doi: 10.1093/ietfec/e90-a.7.1481.
Abstract: This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpass-highpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This means that any transformed system that is generated from a prototype system has the same second-order modes as those of the prototype system. We achieve the derivation of this result by describing the state-space equations and the controllability/observability Gramians of transformed systems.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.7.1481/_p

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@ARTICLE{e90-a_7_1481,
author={Masayuki KAWAMATA, Yousuke MIZUKAMI, Shunsuke KOSHITA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Invariance of Second-Order Modes of Linear Continuous-Time Systems under Typical Frequency Transformations},
year={2007},
volume={E90-A},
number={7},
pages={1481-1486},
abstract={This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpass-highpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This means that any transformed system that is generated from a prototype system has the same second-order modes as those of the prototype system. We achieve the derivation of this result by describing the state-space equations and the controllability/observability Gramians of transformed systems.},
keywords={},
doi={10.1093/ietfec/e90-a.7.1481},
ISSN={1745-1337},
month={July},}

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TY - JOUR
TI - Invariance of Second-Order Modes of Linear Continuous-Time Systems under Typical Frequency Transformations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1481
EP - 1486
AU - Masayuki KAWAMATA
AU - Yousuke MIZUKAMI
AU - Shunsuke KOSHITA
PY - 2007
DO - 10.1093/ietfec/e90-a.7.1481
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2007
AB - This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpass-highpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This means that any transformed system that is generated from a prototype system has the same second-order modes as those of the prototype system. We achieve the derivation of this result by describing the state-space equations and the controllability/observability Gramians of transformed systems.
ER -