Minimization of Frequency-Weighted l2 -Sensitivity Subject to l2 -Scaling Constraints for Two-Dimensional State-Space Digital Filters

This paper investigates the problem of frequencyweighted l2-sensitivity minimization subject to l2-scaling constraints for two-dimensional (2-D) state-space digital filters described by the Roesser model. It is shown that the FornasiniMarchesini second model can be imbedded in the Roesser model. Two iterative methods are developed to solve the constrained optimization problem encountered. The first iterative method introduces a Lagrange function and optimizes it using some matrix-theoretic techniques and an efficient bisection method. The second iterative method converts the problem into an unconstrained optimization formulation by using linear-algebraic techniques and solves it by applying an efficient quasi-Newton algorithm. The optimal filter structure with minimum frequencyweighted l2-sensitivity and no overflow is then synthesized by an appropriate coordinate transformation. Case studies are presented to demonstrate the validity and effectiveness of the proposed techniques.