Weighted pole and zero sensitivity minimization subject to 1_2-scaling constraints for state-space digital filters

Abstract

In this paper, the problem of minimizing a weighted pole and zero sensitivity measure subject to 1_2-norm dynamic range scaling constraints for state-space digital filters is investigated. First, a new measure for evaluating pole and zero sensitivity is introduced, and it is shown that the constrained optimization problem is converted into an unconstrained optimization problem by using linear algebraic techniques. Then, the unconstrained optimization problem at hand is solved iteratively by employing an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. A numerical example is presented to demonstrate the validity and effectiveness of the proposed iterative optimization technique.