This paper presents results from a study to examine the stabilization properties of linear time delay systems and systems depending on a parameter using techniques associated with the algebraic Riccati equation (ARE). These classes of systems can be viewed as members of a broader class of systems called generalized linear systems (GLS). Techniques of spectral factorization for the GLS play an essential role in the methods for performing this stabilization. Necessary and sufficient conditions for the existence of a polynomial solution to the generalized ARE are derived. Numerical examples are given in order to illustrate and clarify the results.