An argument-principle based stability criterion and application to the design of IIR digital filters

A method for the design of IIR digital filters with pole radius constraint based on the argument principle (AP) from complex analysis is proposed. Unlike the stability constraints available in the literature which are sufficient but not necessary stability constraints, the proposed AP-based stability condition is both sufficient and necessary. We show that weighted least-squares and minimax designs of robustly stable IIR filters can be accomplished in convenient convex programming settings where the proposed stability criterion can easily be incorporated as a single equality constraint that does not depend on any parameters other then filter's denominator coefficients. Design examples are presented to illustrate the usefulness of the proposed algorithms.