Algebraic solution to the robust SPR problem for two polynomials

In this paper we provide an algebraic method for the design of an appropriate transfer function making simultaneously two polynomials strictly positive real (SPR), in the so-called robust SPR problem for two polynomials. This problem arises in the design of recursive estimation algorithms used for identi"cation purposes and in active noise control (ANC) applications. In the former a given transfer function involving the poles of the unknown transfer function must be made SPR; in the latter, the phase of a transfer function must be matched within a range of (! /2, /2). Robust SPR design methods try to ful"ll the phase requirements for all possible transfer functions belonging to a given uncertainty description. Here we focus on uncertainties described by two polynomials. 2001 Elsevier Science Ltd. All rights reserved.