A new canonical expansion of z-transfer function for reduced-order modeling of discrete-time systems

On the basis of the unique decomposition of a polynomial into a mirror image polynomial (MIP) and an antimirror image polynomial (AMIP) and the expansion of A.M. Davis´ discrete reactance function (ibid., vol.CAS-29, no.10, p.658-62, 1982) into a continued fraction which proceeds in terms of z/(z-1) and 1/(z-1) alternately, a new canonical expansion of the z-transfer function is presented. Although it has the same structure as the Routh canonical expansion of the s-transfer function, the new canonical expansion is suitable for deriving reduced-order models of discrete-time systems by direct truncation. Using this canonical expansion, frequency- and time-domain reduced-order modeling procedures are derived. The necessary and sufficient conditions imposed on the continued-fraction expansion of Davis´ discrete reactance function for reduced-order models to be stable are also derived. It is shown that the reduced model has the partial Pade approximation property