On Frequency-Weighted l2-Sensitivity Analysis and Minimization of 2-D State-Space Digital Filters Subject to l2-Scaling Constraints

The minimization problem of a frequency-weighted l₂-sensitivity measure subject to l₂-scaling constraints for two-dimensional (2D) state-space digital filters is formulated. First, an iterative method for solving the constrained optimization problem in question is developed by introducing a Lagrange function and applying some matrix-theoretic techniques as well as an efficient bisection method. The optimal filter structure is then synthesized so as to minimize the frequency-weighted l₂-sensitivity subject to l₂-scaling constraints. Finally, a numerical example is presented to illustrate the utility of the proposed technique.