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.
|Number of pages||7|
|Journal||Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (|
|Publication status||Published - 1987 Oct 1|
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