The effect of the delayed feedback control on the stability of periodic solutions of linear systems with sate jump is studied. Although the stability of the open-loop and the OGY feedback cases can be analyzed via matrix representations (Poincare map), the system with DFC requires an operator representation of the state transition on a certain function space due to the infinite-dimensionality caused by the time delay element in the controller. A stability condition is given in terms of the spectrum of this operator. Also an analytic formula and a numerical method for the computation of the spectrum are provided.