Conditions for designing strictly positive real transfer functions for adaptive output error identification

Strictly positive real (SPR) transfer functions are of importance in Adaptive systems theory. This paper addresses two issues related to finding a polynomial such that is SPR for all belonging to a set of th-degree Hurwitz polynomials defined by the magnitude bounds on the coefficients of . It is shown that irrespective of there exist four polynomials in such that if the ratios of with each of these is SPR then is SPR for all members of . A sufficient condition for the existence of this along with a method for its construction is outlined. The condition resembles the Routh array test for determining system stability.