Synthesis of 2-D state-space digital filters with low sensitivity based on the Fornasini-Marchesini model

The balanced realization and low-sensitivity structure of two-dimensional recursive digital filters are considered in the framework of the Fornasini-Marchesini local state-space model. A procedure is introduced for the balanced realization of 2-D recursive digital filters. The sensitivities of a 2-D transfer function are investigated with respect to the coefficients in the local state-space model. The overall sensitivity is evaluated using the 2-D controllability and observability Gramians. The filter structure reducing the overall sensitivity is synthesized for two cases: one free from l₂ scaling constraints on the state variables and the other under the scaling constraints. These filter structures are shown to be closely related to the balanced realization. An example is given to illustrate the utility of the proposed technique