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

Tao LIN  Masayuki KAWAMATA  Tatsuo HIGUCHI  

IEICE TRANSACTIONS (1976-1990)   Vol.E70   No.10   pp.938-944
Publication Date: 1987/10/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Circuit Theory

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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.