In this paper, a method of combining the Routh approximation method with the bilinear transformation is presented for deriving stable reduced-order models of a strictly proper z-transfer function Gn(z). It is based on applying the bilinear transformation to the (z+1)Gn(z), and then deriving a new bilinear Routh γ − δ canonical expansion for Gn(z). The proposed bilinear Routh approximation method has all the advantages of the Routh approximation method [5] while without having initial-value problem caused by the bilinear transformation. A numerical example is included to illustrate the procedure.

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