Abstract
In this paper we consider the differential periodic Riccati equation. All the periodic nonnegative definite solutions are characterized in the more general case, providing a method for constructing them. The method is obtained from the study of the invariant subspaces of the monodromy matrix of the associated Hamiltonian system, and from the relations between these invariant subspaces and the controllability and unobservability subspaces. Finally, the method is applied to obtain necessary and sufficient conditions for the existence of any periodic nonnegative definite solution and to study the existence and uniqueness of minimal, maximal, stabilizing, and strong solutions.
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