Abstract
It is shown that any rational scalar positive real (in the sense of [1]) function of several variables, having degree two of its numerator polynomial, admits the representation in the form of Schur complement of a block of some linear homogeneous matrix bundle with real positive semidefinite matrix coefficients.
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This paper is a translation from the Russian, prepared by D. Kalyuzhnyi-Verbovetzkii, of a part of the second chapter from the author’s Ph. D. thesis entitled “Functions of Several Variables in the Theory of Finite Linear Structures”, Kharkov, 1982. The manuscript, entitled “Realization of Rational Functions of Several Variables by Means of a Long Resolvent” was deposited at VINITI (86 pages, submitted by the Kharkov University, July 8, 1981, No. 3352-81).
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References
M.F. Bessmertnyi, On realization of rational matrix functions of several variables. Oper. Theory: Adv. Appl. 134 (2002), 157–185.
M.F. Bessmertnyi, On realization of rational matrix functions of several variables. II.Oper. Theory: Adv. Appl. 143 (2003).
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Bessmertnyĭ, M.F. (2004). On Realizations of Rational Matrix Functions of Several Variables III. In: Ball, J.A., Helton, J.W., Klaus, M., Rodman, L. (eds) Current Trends in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 149. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7881-4_6
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DOI: https://doi.org/10.1007/978-3-0348-7881-4_6
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