Weighted sensitivity minimization synthesis of 2-D filter structures using the Fornasini-Marchesini second model

Based on the Fornasini-Marchesini second local state-space model, the problem of synthesizing the optimal finite word length 2-D state-space filter structures is considered. First, a frequency-weighted sensitivity measure is defined in place of the usual sensitivity measure. Two techniques are then developed for finding the set of optimal filter structures that minimize this frequency-weighted sensitivity measure over all the similarity transformations. One is analytically round by applying Lagrange´s method and the other is iteratively done by using a gradient method. Finally, a numerical example is given to illustrate the utility of the proposed two techniques