Analysis of Second-Order Modes of Linear Discrete-Time Systems under Bounded-Real Transformations

Shunsuke KOSHITA; Masahide ABE; Masayuki KAWAMATA

doi:10.1093/ietfec/e90-a.11.2510

Analysis of Second-Order Modes of Linear Discrete-Time Systems under Bounded-Real Transformations

Shunsuke KOSHITA, Masahide ABE, Masayuki KAWAMATA

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This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless bounded-real transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.11 pp.2510-2515

Publication Date: 2007/11/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e90-a.11.2510

Type of Manuscript: PAPER

Category: Systems and Control

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Shunsuke KOSHITA, Masahide ABE, Masayuki KAWAMATA, "Analysis of Second-Order Modes of Linear Discrete-Time Systems under Bounded-Real Transformations" in IEICE TRANSACTIONS on Fundamentals, vol. E90-A, no. 11, pp. 2510-2515, November 2007, doi: 10.1093/ietfec/e90-a.11.2510.
Abstract: This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless bounded-real transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.11.2510/_p

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@ARTICLE{e90-a_11_2510,
author={Shunsuke KOSHITA, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Analysis of Second-Order Modes of Linear Discrete-Time Systems under Bounded-Real Transformations},
year={2007},
volume={E90-A},
number={11},
pages={2510-2515},
abstract={This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless bounded-real transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.},
keywords={},
doi={10.1093/ietfec/e90-a.11.2510},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - Analysis of Second-Order Modes of Linear Discrete-Time Systems under Bounded-Real Transformations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2510
EP - 2515
AU - Shunsuke KOSHITA
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2007
DO - 10.1093/ietfec/e90-a.11.2510
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2007
AB - This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless bounded-real transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.
ER -