On convex stability domain and optimization of IIR filters

We discuss descriptions of convex domains containing Schur polynomials, built around a given Schur polynomial. We show that the domain described by a positive realness constraint always contains the domain characterized by Rouché's theorem. We also show how to handle computationally the positive realness condition, using semidefinite programming, in the context of designing stable IIR filters. Two recent methods of Lang [4] and Lu et al [6] for optimizing IIR filters according to a least-squares criterion are modified to incorporate the positive realness condition and shown experimentally to give similar results.