Minimization of Weighted Pole and Zero Sensitivity for State-Space Digital Filters

This paper presents a systematic study of pole and zero sensitivity minimization for state-space digital filters in several different yet related settings. First, a new weighted measure for pole and zero sensitivity for state-space digital filters is proposed and the problem of minimizing this measure is investigated. To this end, two efficient iterative techniques for minimizing this measure are developed by employing a quasi-Newton algorithm and relying on a recursive matrix equation, respectively. Furthermore, minimization of the proposed sensitivity measure subject to l(2)-scaling constraints is examined by extending the two aforementioned solution methods-one converts the constrained optimization problem at hand into an unconstrained problem and solves it using a quasi-Newton algorithm, while the other relaxes the constraints into a single constraint on matrix trace and solves the relaxed problem with an effective matrix iteration scheme. In addition, a simple yet novel method for the minimization of a zero sensitivity measure subject to minimal pole sensitivity is explored by pursuing an optimal coordinate transformation matrix. Simulation studies are presented to demonstrate the validity and effectiveness of the proposed techniques.