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.