  Controlled frames and g-frames were considered recently as generalizations of
frames in Hilbert spaces. In this paper we generalize some of the known results
in frame theory to controlled g-frames. We obtain some new properties of
controlled g-frames and obtain new controlled g-frames by considering
controlled g-frames for its components. And we obtain some new resolutions of
the identity. Furthermore, we study the stabilities of controlled g-frames
under small perturbations.
