Computation of the (j, j′)-lossless factorization for general rational matrices

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)240-267
Journal / PublicationSIAM Journal on Control and Optimization
Issue number1
Publication statusPublished - 2006


(J, J′)-lossless factorization plays a central role in H -control because it gives a simple and unified framework of H-control from the viewpoint of classical network theory, and it includes the well-known inner-outer factorization of rational matrices, Wiener-Hopf factorization, and spectral factorization of positive rational matrices as special cases. However, up to now, there is still a lack of numerically reliable methods for this important factorization problem in a general setting. In this paper, we present necessary and sufficient solvability conditions and develop a numerically reliable algorithm based on a generalized eigenvalue approach for the (J, J′)-lossless factorization of general rational matrices. © 2005 Society for Industrial and Applied Mathematics.

Research Area(s)

  • (j, j′)-lossless factorization, Eigenfactorization orthogonal transformation, Rational matrix