Periodic Riccati equation: A decomposition approach

In this paper, the periodic Riccati equation is considered. It is proved that a unique periodic positive semidefinite solution exists and the associated closed-loop system is asymptotically stable if and only if the underlying periodic system is stabilizable and detectable. The proof is based on the decomposition of the Riccati equation obtained by considering the system decomposed in the Kalman canonical form. Such a technique allows pointing out some nice structural properties of the positive semidefinite solution.