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Analytic Interpolation With a Degree Constraint for Matrix-Valued Functions

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2 Author(s)
Takyar, M.S. ; Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Minneapolis, MN, USA ; Georgiou, T.T.

We consider a Nehari problem for matrix-valued, positive-real functions, and characterize the class of (generically) minimal-degree solutions. Analytic interpolation problems (such as the one studied herein) for positive-real functions arise in time-series modeling and system identification. The degree of positive-real interpolants relates to the dimension of models and to the degree of matricial power-spectra of vector-valued time-series. The main result of the paper generalizes earlier results in scalar analytic interpolation with a degree constraint, where the class of (generically) minimal-degree solutions is characterized by an arbitrary choice of ??spectral-zeros??. Naturally, in the current matricial setting, there is freedom in assigning the Jordan structure of the spectral-zeros of the power spectrum, i.e., the spectral-zeros as well as their respective invariant subspaces. The characterization utilizes Rosenbrock's theorem on assignability of dynamics via linear state feedback.

Published in:

Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 5 )

Date of Publication:

May 2010

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