Multivariable partial realization and the aspect of uniqueness

This paper deals with the minimal partial realization problem for a multivariable power series of finite length. Specifically, the problem of the uniqueness of the extension sequence is considered and a fundamental criterion is given which is necessary and sufficient for the existence of a unique extension. A specific class of formal power series is introduced (finite generic sequences) for which the criterion mentioned above takes a very simple form. This class is of interest when considering the availability of a sequence of noise distributed Markov parameters of a multivariable system. Finally the approximate partial realization problem is defined.