The extended J-spectral factorization for descriptor systems
Automatica (Journal of IFAC)
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J,J'-lossless factorization plays a central role in $H_\infty$-control because it gives a simple and unified framework of $H_\infty$-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.