L2-sensitivity minimization of one- and two-dimensional state-space digital filters subject to L2-scaling constraints

Abstract — We investigate the problem of minimizing an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints for one-dimensional (1-D) as well as a class of two-dimensional (2-D) state-space digital filters, where the 2-D digital filters are described by a transposed structure of the Fornasini-Marchesini second local state-space model. In each case, a novel iterative technique is developed to solve the constraint optimiza-tion problem directly. Our solution methods are largely based on the use of a Lagrange function and some matrix-theoretic techniques. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques. Index Terms—L2-sensitivity minimization, L2-norm dynamic-range scaling constraints, Lagrange’s function, optimal realiza-tion, state-space digital filters, a class of 2-D state-space digital filters. I