\((J,J')\)-spectral factorization and conjugation for discrete-time descriptor system (Q2563556)

A \((J,J')\)-spectral factorization algorithm associated with stable improper transfer matrices based on the generalized algebraic Riccati equation is derived. A numerical method based on the solutions of the associated generalized eigenvalue problem and an auxiliary linear equation is presented. A method for computing a \(J\)-unitary conjugator of an unstable transfer matrix to get a \((J,J')\)-spectral factor of the signed spectral matrix is developed. A Hankel norm model reduction is also considered. The considerations are illustrated by a numerical example.