The purpose of this paper is to develop a novel approach to the problem of spectral factorization of matrix-valued functions. The key idea first appeared in Georgiou and Khargonekar ,  where results were obtained for the scalar case. We exploit a version of the Nevanlinna-Pick algorithm that applies to matrix-valued functions and we make use of results in interpolation theory with matrix-valued functions analytic on The unit disc.
Bibliographical noteFunding Information:
October 4, 1988. This work was supported in part by the National Science Foundation under Grant MIP-8708811, under Grant ECS-8705291, under Grant ECS-8451519, and in part by grants from Honey-well, Inc., 3M Corporation, and the MEIS Center at the University of Minnesota. This paper was recommended by Associate Editor R. W.L iu. T. T. Georgiou is with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011. p. p. uagoneka is with the of Electrical University of Minnesota, Minneapolis, MN 55455. IFEE Log Number 8826274.
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