Minimal Pade´ Model Reduction for Multivariable Systems

The approximation of high order linear multivariable systems in the Pade´ sense is considered. A unified treatment is presented by which various models of minimal order are found which match given sequences of time moments and Markov matrices. The uniqueness of these models is investigated and in cases where there exist more than one minimal model for a given sequence the set of all the distinct models is characterized by a minimal set of independent parameters which can be assigned arbitrary values. The possible instability of Pade´ reduced models for stable systems is considered and a method is suggested which yields stable models that approximate the high order system, or at least its magnitude, in the Pade´ sense.