Abstract
The Loewner approach, based on the factorization of a special-structure matrix derived from data generated by a dynamical system, has been applied successfully to realization theory, generalized interpolation, and model reduction. We examine some connections between such approach and that based on bilinear- and quadratic differential forms arising in the behavioral framework.
Dedicated to Prof. Harry L. Trentelman- friend, colleague, and for the first author also co-supervisor- on the occasion of his “sixtieth birthday”
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Acknowledgments
The authors would like to thank Prof. Dr. A.J. van der Schaft for stimulating discussions.
The results presented here were obtained during the second author’s visit (supported by a travel grant of the UK Engineering and Physical Sciences Research Council) to the Jan C. Willems Center for Systems and Control, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, The Netherlands.
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Rapisarda, P., Antoulas, A.C. (2015). Bilinear Differential Forms and the Loewner Framework for Rational Interpolation. In: Belur, M., Camlibel, M., Rapisarda, P., Scherpen, J. (eds) Mathematical Control Theory II. Lecture Notes in Control and Information Sciences, vol 462. Springer, Cham. https://doi.org/10.1007/978-3-319-21003-2_2
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