L 2-Sensitivity Minimization of One-and Two-Dimensional State – Space Digital Filters Subject to L 2-Scaling Constraints

This paper investigates the problem of minimizing an 2-sensitivity measure subject to 2-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 optimization problem directly. The proposed 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.

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