The descriptor continuous-time algebraic Riccati equation: Numerical solution and application

We investigate the numerical solution of a special type of descriptor continuous-time Riccati equation which is key to several problems in robust control formulated for a general system. We give necessary and sufficient existence conditions together with computable formulas for both stabilizing and antistabilizing solutions in terms of an associated matrix pencil. Analytic formulas for computing normalized coprime factorizations of a general system are presented as a direct application.