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On the embedding of state space realizations

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Abstract

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.

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  1. FSA, Faculté des Sciences Appliquées, Université catholique de Louvain, 1, Place de I’Université B-1348, Louvain-la-Neuve, Belgium

    Yves Genin & Antoine Vandendorpe

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  1. Yves Genin
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  2. Antoine Vandendorpe
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Correspondence to Yves Genin.

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Genin, Y., Vandendorpe, A. On the embedding of state space realizations. Math. Control Signals Syst. 19, 123–149 (2007). https://doi.org/10.1007/s00498-006-0011-3

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  • DOI: https://doi.org/10.1007/s00498-006-0011-3

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