Stable denominators for the simplification of z-transfer functions (Q1061710)

A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates \(m_ 1\) and \(m_ 2=m-m_ 1\) zeros of D(z), located very near the points \(z=1\) and \(z=-1\), respectively. In the special case \(m_ 1=m\), d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method.