  In this paper we discuss how to decompose the constrained generalized
discrete-time algebraic Riccati equation arising in optimal control and optimal
filtering problems into two parts corresponding to an additive decomposition
X=X0+D of each solution X: The first part is an explicit expression of the
addend X0 which is common to all solutions, and does not depend on the
particular X. The second part can be either a reduced-order discrete-time
regular algebraic Riccati equation whose associated closed-loop matrix is
non-singular, or a symmetric Stein equation.
