Minimal pad?? model reduction of multivariable systems

The approximation of high order linear multivariable system in the Pad?? sense is considered. Models of minimal order are found which match given input-output sequences of time moments and Markov matrices. The uniqueness of these models is investigated, and in cases where there exists 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. A unified treatment is presented by which models of the same minimal order that put different emphasis on the approximation at low and high frequencies are obtained. The possible instability of Pad?? reduced models for stable systems is considered and a procedure is suggested which yields stable models that approximate the high order system or at least its magnitude in the Pad?? sense.