J-spectral factorization of regular para-Hermitian transfer matrices

This paper characterizes a class of regular para-Hermitian transfer matrices and then reveals the elementary characteristics of J-spectral factorization for this class. A transfer matrix Λ 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 Λ and Λ-1, resp., into 2×2 lower (upper, resp.) triangular block matrices with the (1,1)-block including all the stable modes of Λ (Λ-1, resp.). For a transfer matrix in a smaller subset, this 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.