Generalized partial realizations
نویسنده
چکیده
In this paper we extend Kalman's concept of partial realization and deene generalized partial realizations of nite matrix sequences by descriptor systems. Our deenition is in agreement with the realization theory for deterministic boundary value descriptor systems 15]. The aim of this contribution is to prove a counterpart of Kalman's main theorem of realization theory for generalized partial realizations. It is shown that every nite scalar sequence possesses a generalized partial realization of minimal dimension rank H where H is an associated Hankel matrix. The same statement holds true for nite sequences of p m matrices provided that one of the associated Hankel matrices has a rank strictly smaller than its numbers of block rows and block columns. The paper ends with some results concerning topological aspects of generalized partial realizations.
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