Analysis of l2-sensitivity for canonical forms in 1-D and 2-D separable-denominator digital filters

Based on a pure l₂ norm, the l₂-sensitivity for canonical forms in one-dimensional (1-D) and two-dimensional (2-D) separable-denoninator state-space digital filters is analyzed more precisely by taking into account 0 and 1 elements. First, l₂-sensitivity measures are explored for a controllable canonical form as well as an observable canonical form in state-space digital filters. Next, an l₂-sensitivity measure is investigated for a canonical form in 2-D separable-denominator state-space digital filters. Finally, numerical examples are presented to compare the resulting l₂-sensitivity measures with the conventional ones.