  K-frames were recently introduced by L. G\v{a}vruta 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 efficiency 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.
