Minimization of L2-Sensitivity for 2-D Separable-Denominator State-Space Digital Filters Subject to L2-Scaling Constraints

For two-dimensional (2D) separable-denominator state-space digital filters, the minimization problem of an L
₂
-sensitivity measure subject to L
₂
-scaling constraints was investigated. First, the coefficient sensitivity is analyzed by using a pure L
₂
norm. Next, an iterative algorithm is developed for minimizing an L
₂
-sensitivity measure subject to L
₂
-scaling constraints. This approach largely relies on the use of a Lagrange function and some matrix-theoretic techniques