Minimization of L2-sensitivity for a class of 2D state-space digital filters subject to L2-scaling constraints

The paper is concerned with the minimization of an L₂-sensitivity measure subject to L₂-norm dynamic range scaling constraints for a class of two-dimensional (2D) state-space digital filters. A novel iterative algorithm is developed to solve the constrained optimization problem directly. The proposed solution method is largely based on the use of a Lagrange function and some matrix theoretic techniques. A numerical example is presented to demonstrate the utility of the proposed technique.