Spectral factorization of singular systems using generalized algebraic Riccati equations

The spectral factorization of singular systems consisting of tall and rational proper systems with invariant zeros on the jω-axis (including infinity) is derived. This is achieved by solving a generalized algebraic Riccati equation (GARE), which is solved by a generalized eigenvector problem. In this work, zero compensators proposed by Goh et al. are not used, and the results are applied to the inner-outer factorization problem in order to provide simple state space realizations for the inner and outer functions