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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.


This is a preprint draft of an article that was accepted for publication in Linear Algebra and its Applications, volume 580, in 2019 following peer review, and may not exactly replicate the final published version. The definitive publisher-authenticated version is available online at DOI: 10.1016/j.laa.2019.06.014.





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