Simplified computation of l2-sensitivity for 1-D and a class of 2-D state-space digital filters considering 0 and ±1 elements

A simplified method of computing an improved l₂-sensitivity measure is developed for state-space digital filters by reducing the number of the Lyapunov equations, and it is expanded into a class of two-dimensional (2-D) state-space digital filters. First, a conventional improved l₂-sensitivity for state-space digital filters is reviewed and simplified to two novel forms so that the number of the Lyapunov equations is reduced. Next, the resulting mehod is expanded into a class of 2-D state-space digital filters. Finally, two numerical examples are presented to evaluate more precise (improved) l₂-sensitivity measures for 1-D and a class of 2-D state-space digital filters by employing the proposed methods.