  Controlled frames have been the subject of interest because of its ability to
improve the numerical efficiency of iterative algorithms for inverting the
frame operator. In this paper, we introduce the notion of controlled $K$-frame
in Hilbert $C^{*}$-modules. We establish the equivalent condition for
controlled $K$-frame. We investigate some operator theoretic characterizations
of controlled $K$-frames and controlled Bessel sequences. Moreover we establish
the relationship between the $K$-frames and controlled $K$-frames. We also
investigate the invariance of a $C$-controlled $K$-frame under a suitable map
$T$. At the end we prove a perturbation result for controlled
$K$-frame.Controlled frames have been the subject of interest because of its
ability to improve the numerical efficiency of iterative algorithms for
inverting the frame operator. In this paper, we introduce the notion of
controlled $K$-frame in Hilbert $C^{*}$-modules. We establish the equivalent
condition for controlled $K$-frame. We investigate some operator theoretic
characterizations of controlled $K$-frames and controlled Bessel sequences.
Moreover we establish the relationship between the $K$-frames and controlled
$K$-frames. We also investigate the invariance of a $C$-controlled $K$-frame
under a suitable map $T$. At the end we prove a perturbation result for
controlled $K$-frame.
