K-frames were recently introduced by L. Gavruta in Hilbert spaces to study atomic systems with respect to bounded linear operator. Also controlled frames have been recently introduced by Balazs, Antoine and Grybos in Hilbert spaces to improve the numerical eciency of interactive algorithms for inverting the frame operator. In this manuscript, the concept of controlled K-frames will be studied and the stability of Controlled K-frames under compact perturbation will be discussed.
