  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 P. Balazs in Hilbert spaces to improve
the numerical efficiency of interactive algorithms for inverting the frame
operator. In this manuscript, we will define the concept of the controlled
K-frames and will show that controlled K-frames are equivalent to K-frames and
so the controlled operator C can be used as preconditions in applications.
