Abstract This paper deals with the H ∞ FI control problem for continuous-time linear periodic systems. It is proven a necessary and sufficient condition for the existence of a T-periodic controller which internally stabilizes the given system and satisfies a constraint on the H ∞ norm of the closed-loop system. Intriguing questions arise when dealing with the parametrization problem for such controllers. The results provided herein calls for the properties of T-periodic Riccati equaticns and the structural properties of a periodic systems