TY - JOUR

T1 - MINIMIZATION OF SENSITIVITY OF 2-D SYSTEMS AND ITS RELATION TO 2-D BALANCED REALIZATIONS.

AU - Lin, Tao

AU - Kawamata, Masayuki

AU - Higuchi, Tatsuo

PY - 1987/10/1

Y1 - 1987/10/1

N2 - 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 constant 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 the sensitivity is equivalent to the minimization of roundoff noise under l//2-norm scaling constraint. An example shows the method of analyzing and minimizing the sensitivity of 2-D systems.

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 constant 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 the sensitivity is equivalent to the minimization of roundoff noise under l//2-norm scaling constraint. An example shows the method of analyzing and minimizing the sensitivity of 2-D systems.

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M3 - Article

AN - SCOPUS:0023440045

VL - E70

SP - 938

EP - 944

JO - Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (

JF - Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (

IS - 10

ER -