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On multivariable proper rational interpolation using coprime factors

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Abstract

We analyse and construct the matrix-valued proper rational solutions of the tangential interpolation problem. We show how the coprime polynomial factorization of the solutions is tightly connected to the controllability indices of a pair \(({\mathscr {A}},[U,V])\) associated with the interpolation data and that coprimeness of these factorizations is guaranteed by a simple condition on the eigenvectors of \({\mathscr {A}}\).

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Acknowledgements

The research was partially supported by a Bilateral Research Project agreement between CNR and MTA for the triennium 2010–2012.

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Authors and Affiliations

  1. Eötvös Loránd University, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary

    Gy. Michaletzky

  2. IEIIT-CNR, Via Giovanni Gradenigo 6a, 35131, Padua, Italy

    A. Gombani

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  1. Gy. Michaletzky
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  2. A. Gombani
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Correspondence to Gy. Michaletzky.

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Michaletzky, G., Gombani, A. On multivariable proper rational interpolation using coprime factors. Math. Control Signals Syst. 30, 8 (2018). https://doi.org/10.1007/s00498-018-0215-3

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  • DOI: https://doi.org/10.1007/s00498-018-0215-3

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