Sub-optimal discrete model reduction by multipoint Padé approximation

A multipoint Padé approximation method is presented for obtaining a reduced order z-transfer function, with a pre-determined denominator, such that the square-error-sum of time responses between the full and reduced models is minimized. An extension of the method to matching the initial time response values for impulse and step inputs is also given. The method and its extension are seen to be easy to apply and are very amenable to use on modern computer algebra systems, consisting entirely of simple matrix operations. Numerical examples are given to illustrate the application of the technique.