Numerical solution to a descriptor discrete-time algebraic Riccati equation

We investigate the numerical solution of a special type of descriptor discrete-time Riccati equation involved in the solution of several key problems in robust control formulated under very general hypotheses. Necessary and sufficient existence conditions together with computable formulas are given for the stabilizing and antistabilizing solutions in terms of an associated matrix pencil. Two particular applications and numerical experiments of our results are included for squaring-down with L∞L∞ norm preservation and (J,J′)(J,J′)-spectral factorization, both for a completely general discrete-time system.