A generalized on the study synthesis of 2-D state-space digital filters with minimum roundoff noise

The Fornasini-Marchesini local state-space (LSS) model is used as the basis for a novel expression for the output-noise variance due to roundoff together with an I₂ scaling on the state variables. An optimal Fornasini-Marchesii LSS model structure is then synthesized that minimizes the output noise due to roundoff, subject to an l₂ scaling constraint. The synthesis utilizes a 2-D similarity transformation matrix that is not block-diagonal, but general. This requires solving only one optimization problem. Some constraints imposed on the Fornasini-Marchesini LSS model and the 2-D similarity transformation yield the results obtained with the Roesser LSS model. The proposed synthesis theory is therefore quite general and simple. An example is given to illustrate its utility