  The recently introduced concept of $E$-frames for a separable Hilbert space
$\mathcal{H}$, where E is an invertible infinite matrix mapping on the Hilbert
space $\bigoplus_{n=1}^{\infty}\mathcal{H}$, is a generalization of the notion
of frames for $\mathcal{H}$. In this paper, we have stated some results about
this concept. Furthermore, we introduce the notion of controlled $E$-frames and
we characterize all controlled $E$-duals associated with a given controlled
$E$-frame.
