Spectral and inner-outer factorizations through the constrained Riccati equation

The topic of the paper is the spectral factorization problem for a proper rational matrix function of constant rank, but not necessarily maximal, on the extended imaginary axis. The problem is reduced to the computation of the stabilizing solution of a so-called constrained Riccati equation. The proof of the main result suggests a Schur-like algorithm applied to a singular matrix pencil