Minimization of Sensitivity of 2-D Systems and Its Relation to 2-D Balanced Realizations

Tao LIN; Masayuki KAWAMATA; Tatsuo HIGUCHI

Minimization of Sensitivity of 2-D Systems and Its Relation to 2-D Balanced Realizations

Tao LIN, Masayuki KAWAMATA, Tatsuo HIGUCHI

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The average coefficient sensitivity is defined for 2-D systems described by Roesser's local state space model. The sensitivity can be computed by using the 2-D observability Gramian and the 2-D controllability Gramian, which are also called the 2-D noise matrix and the 2-D covariance matrix if the 2-D systems are considered to be 2-D digital filters. Minimization of sensitivity via 2-D equivalent transforms is studied in cases of having no constraint and having a scaling constraint on the state vector. In the first case, the minimum sensitivity realizations are equivalent to the 2-D balanced realizations modulo a block orthogonal transform. In the second case, the 2-D systems are considered to be 2-D digital filters and the minimization of sensitivity is equivalent to the minimization of roundoff noise under l₂-norm scaling constraint. An example is given to show method of analysing and minimizing the sensitivity of 2-D systems.

Publication: IEICE TRANSACTIONS on transactions Vol.E70-E No.10 pp.938-944

Publication Date: 1987/10/25

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Type of Manuscript: PAPER

Category: Circuit Theory

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Tao LIN
Masayuki KAWAMATA
Tatsuo HIGUCHI

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Tao LIN, Masayuki KAWAMATA, Tatsuo HIGUCHI, "Minimization of Sensitivity of 2-D Systems and Its Relation to 2-D Balanced Realizations" in IEICE TRANSACTIONS on transactions, vol. E70-E, no. 10, pp. 938-944, October 1987, doi: .
Abstract: The average coefficient sensitivity is defined for 2-D systems described by Roesser's local state space model. The sensitivity can be computed by using the 2-D observability Gramian and the 2-D controllability Gramian, which are also called the 2-D noise matrix and the 2-D covariance matrix if the 2-D systems are considered to be 2-D digital filters. Minimization of sensitivity via 2-D equivalent transforms is studied in cases of having no constraint and having a scaling constraint on the state vector. In the first case, the minimum sensitivity realizations are equivalent to the 2-D balanced realizations modulo a block orthogonal transform. In the second case, the 2-D systems are considered to be 2-D digital filters and the minimization of sensitivity is equivalent to the minimization of roundoff noise under l₂-norm scaling constraint. An example is given to show method of analysing and minimizing the sensitivity of 2-D systems.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e70-e_10_938/_p

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@ARTICLE{e70-e_10_938,
author={Tao LIN, Masayuki KAWAMATA, Tatsuo HIGUCHI, },
journal={IEICE TRANSACTIONS on transactions},
title={Minimization of Sensitivity of 2-D Systems and Its Relation to 2-D Balanced Realizations},
year={1987},
volume={E70-E},
number={10},
pages={938-944},
abstract={The average coefficient sensitivity is defined for 2-D systems described by Roesser's local state space model. The sensitivity can be computed by using the 2-D observability Gramian and the 2-D controllability Gramian, which are also called the 2-D noise matrix and the 2-D covariance matrix if the 2-D systems are considered to be 2-D digital filters. Minimization of sensitivity via 2-D equivalent transforms is studied in cases of having no constraint and having a scaling constraint on the state vector. In the first case, the minimum sensitivity realizations are equivalent to the 2-D balanced realizations modulo a block orthogonal transform. In the second case, the 2-D systems are considered to be 2-D digital filters and the minimization of sensitivity is equivalent to the minimization of roundoff noise under l₂-norm scaling constraint. An example is given to show method of analysing and minimizing the sensitivity of 2-D systems.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Minimization of Sensitivity of 2-D Systems and Its Relation to 2-D Balanced Realizations
T2 - IEICE TRANSACTIONS on transactions
SP - 938
EP - 944
AU - Tao LIN
AU - Masayuki KAWAMATA
AU - Tatsuo HIGUCHI
PY - 1987
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E70-E
IS - 10
JA - IEICE TRANSACTIONS on transactions
Y1 - October 1987
AB - The average coefficient sensitivity is defined for 2-D systems described by Roesser's local state space model. The sensitivity can be computed by using the 2-D observability Gramian and the 2-D controllability Gramian, which are also called the 2-D noise matrix and the 2-D covariance matrix if the 2-D systems are considered to be 2-D digital filters. Minimization of sensitivity via 2-D equivalent transforms is studied in cases of having no constraint and having a scaling constraint on the state vector. In the first case, the minimum sensitivity realizations are equivalent to the 2-D balanced realizations modulo a block orthogonal transform. In the second case, the 2-D systems are considered to be 2-D digital filters and the minimization of sensitivity is equivalent to the minimization of roundoff noise under l₂-norm scaling constraint. An example is given to show method of analysing and minimizing the sensitivity of 2-D systems.
ER -