Composition of rational functions: state-space realization and applications

Daniel Alpay; Izchak Lewkowicz

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arXiv · 1807.01753

Composition of rational functions: state-space realization and applications

Daniel Alpay·Izchak Lewkowicz

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Abstract

We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the original functions. Focusing on positive real functions, the first composition is applied to electrical circuits theory along with introducing a connection to networks of feedback loops. The second composition is applied to Stieltjes functions.

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Daniel Alpay, Izchak Lewkowicz. 2018-07-04. Composition of rational functions: state-space realization and applications. https://arxiv.org/abs/1807.01753

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