Gramian-Preserving Frequency Transformation for Linear Discrete-Time State-Space Systems
Summary :
This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.10 pp.3014-3021
- Publication Date
- 2008/10/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e91-a.10.3014
- Type of Manuscript
- PAPER
- Category
- Systems and Control
Authors
Keyword
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Shunsuke KOSHITA, Satoru TANAKA, Masahide ABE, Masayuki KAWAMATA, "Gramian-Preserving Frequency Transformation for Linear Discrete-Time State-Space Systems" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 10, pp. 3014-3021, October 2008, doi: 10.1093/ietfec/e91-a.10.3014.
Abstract: This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.10.3014/_p
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@ARTICLE{e91-a_10_3014,
author={Shunsuke KOSHITA, Satoru TANAKA, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Gramian-Preserving Frequency Transformation for Linear Discrete-Time State-Space Systems},
year={2008},
volume={E91-A},
number={10},
pages={3014-3021},
abstract={This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems.},
keywords={},
doi={10.1093/ietfec/e91-a.10.3014},
ISSN={1745-1337},
month={October},}
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TY - JOUR
TI - Gramian-Preserving Frequency Transformation for Linear Discrete-Time State-Space Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3014
EP - 3021
AU - Shunsuke KOSHITA
AU - Satoru TANAKA
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2008
DO - 10.1093/ietfec/e91-a.10.3014
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2008
AB - This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems.
ER -
English
