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On the embedding of state space realizations

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Genin, Yves [UCL] Vandendorpe, Antoine

In this paper, the generality of the particular model reduction method, known as the projection of state space realization, is investigated. Given two transfer functions, one wants to find the necessary and sufficient conditions for the embedding of a state-space realization of the transfer function of smaller McMillan degree into a state-space realization of the transfer function of larger McMillan degree. Two approaches are considered, both in the MIMO case. First, when the difference of the McMillan degree between the transfer functions is equal to one and there is no common pole, necessary and sufficient conditions are provided. Then, the generic case is considered using a pencil approach. Finally, it is shown that the condition of embedding is related to the eigen structure of a pencil that appears in the framework of tangential interpolation.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2007
Language Anglais
Journal information "Mathematics of Control, Signals and Systems" - Vol. 19, no. 2, p. 123-149 (2007)
Peer reviewed yes
Publisher Springer London Ltd (Artington)
issn 0932-4194
e-issn 1435-568X
Publication status Publié
Affiliation UCL
Keywords model order reduction ; linear time invariant system ; truncation technique ; embedding ; state space
Links
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Bibliographic reference Genin, Yves ; Vandendorpe, Antoine. On the embedding of state space realizations. In: Mathematics of Control, Signals and Systems, Vol. 19, no. 2, p. 123-149 (2007)
Permanent URL http://hdl.handle.net/2078.1/37621