Padé methods of Hurwitz polynomial approximation with application to linear system reduction

Two Padé methods are discussed for constructing low-degree Hurwitz polynomials from a given high-degree Hurwitz polynomial to approximate its argument. Using the Hurwitz polynomial approximants as characteristic polynomials, the numerator dynamics of reduced-order (matrix) transfer-function models are then easily determined by partial Padé approximation of a given large-order model. Stability of such reduced models is always assured. By suitable linear fractional transformations the methods are made applicable to discrete-time systems. The methods are compared in simulation examples for both continuous and discrete-time systems.