Abstract.
We introduce a class of matrix-valued functions W called “L2- regular”. In case W is J-inner, this class coincides with the class of “strongly regular J-inner” matrix functions in the sense of Arov–Dym. We show that the class of L2-regular matrix functions is exactly the class of transfer functions for a discrete-time dichotomous (possibly infinite-dimensional) input-state-output linear system having some additional stability properties. When applied to J-inner matrix functions, we obtain a state-space realization formula for the resolvent matrix associated with a generalized Schur–Nevanlinna–Pick interpolation problem.
Communicated by Daniel Alpay
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Submitted: August 20, 2006; Accepted: September 13, 2006
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Ball, J.A., Raney, M.W. Discrete-Time Dichotomous Well-Posed Linear Systems and Generalized Schur–Nevanlinna–Pick Interpolation. Complex anal.oper.theory 1, 1–54 (2007). https://doi.org/10.1007/s11785-006-0001-y
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DOI: https://doi.org/10.1007/s11785-006-0001-y