A note on the maximal solution of the periodic Riccati equation

The periodic symmetric solutions of the periodic Riccati differential equation associated with the filtering problem are considered by the authors. It is proven that, under the sole assumption of detectability, there exists a maximal solution. Moreover, such a solution turns out to be strong, i.e. the characteristic multipliers of the associated closed-loop system belong to the closed unit disk. The proof relies on an iterative linearization technique, which calls for a sequence of periodic Lyapunov equations. Similar results are given for the minimal solution