Synthesis of 2-D state-space filter structures with low frequency-weighted sensitivity

Based on the Roesser (1975) local state-space (LSS) model, new measures are introduced to describe over a particular frequency region the sensitivities of a two-dimensional (2-D) transfer function with respect to state-space parameters. The overall sensitivity derived from these measures is called the frequency weighted sensitivity and is evaluated using 2-D generalized controllability and observability Gramians that are newly defined for 2-D state-space digital filters. Then, 2-D filter structures that minimize the frequency weighted sensitivity are synthesized for two cases of no constraint and scaling constraints on the state variables. These 2-D filter structures can also be optimized with respect to the scaling parameters in the latter case. An example is given to illustrate the utility of the proposed technique