Abstract
A state space description is given of all stable rational matrix solutions of a general rational Bezout type equation on the right half-plane. Included are a state space formula for a particular solution satisfying a certain H 2 minimality condition, a state space formula for the inner function describing the null space of the multiplication operator corresponding to the Bezout equation, and a parameterization of all solutions using the particular solution and this inner function. A state space version of the related Tolokonnikov lemma is also presented.
Mathematics Subject Classification (2010). Primary 47B35, 39B42; Secondary 47A68, 93B28
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Dedicated to Leonia Lerer on the occasion of his 70th birthday, in friendship
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Frazho, A.E., Kaashoek, M.A., Ran, A.C.M. (2013). Rational Matrix Solutions of a Bezout Type Equation on the Half-plane. In: Kaashoek, M., Rodman, L., Woerdeman, H. (eds) Advances in Structured Operator Theory and Related Areas. Operator Theory: Advances and Applications, vol 237. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0639-8_11
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DOI: https://doi.org/10.1007/978-3-0348-0639-8_11
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