Minimal L2 sensitivity realizations of 2-D systems represented with Fornasini-Marchesini LSS model

The optimal state-space realization design problem is investigated in terms of minimizing a frequency weighted L₂-sensitivity measure for two-dimensional (2-D) linear digital systems represented with the Fornasini-Marchesini local state-space (LSS) model. An expression is derived for the transfer function error due to finite word length (FWL) effects on parameters. The optimal realization problem is then formulated, which is shown to be equivalent to minimizing the frequency weighted L₂-sensitivity measure. The problem is solved and the optimal design procedures are illustrated with an example