Minimization of weighted sensitivity for 2-D state-space digital filters described by the Fornasini-Marchesini second model

This paper considers the problem of minimizing the weighted coefficient sensitivity for 2-D state-space digital filters described by the Fornasini-Marchesini (F-M) second model. First, a simple technique is presented for obtaining a set of filter structure with very low weighted L₁/L₂-sensitivity. Next, an iterative procedure is applied to obtain the optimal coordinate transformation that minimizes the weighted L₂-sensitivity measure. This is based on the matrix Riccati differential equation. Finally, a numerical example is given to illustrate the utility of the proposed technique