J-Spectral Factorization via Similarity Transformations

This paper characterizes a class of regular para-Hermitian transfer matrices and then studies the J-spectral factorization of this class using similarity transformations. A transfer matrix in this class admits a J-spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of this transfer matrix and its inverse, resp., into 2 × 2 lower (upper, resp.) triangular block matrices with the (1, 1)-block including all the stable modes of this transfer matrix (its inverse, resp.). For a transfer matrix in a smaller subset, this common nonsingular matrix is formulated in terms of the stabilizing solutions of two algebraic Riccati equations. The J-spectral factor is formulated in terms of the original realization of the transfer matrix.