  This paper studies a class of linear unconditionally energy stable schemes
for the gradient flows. Such schemes are built on the SAV technique and the
general linear time discretization (GLTD) as well as the linearization based on
the extrapolation for the nonlinear term, and may be arbitrarily high-order
accurate and very general, containing many existing SAV schemes and new SAV
schemes. It is shown that the semi-discrete-in-time schemes are unconditionally
energy stable when the GLTD is algebraically stable, and are convergent with
the order of $\min\{\hat{q},\nu\}$ under the diagonal stability and some
suitable regularity and accurate starting values, where $\hat{q}$ is the
generalized stage order of the GLTD and $\nu$ denotes the number of the
extrapolation points in time. The energy stability results can be easily
extended to the fully discrete schemes, for example, if the Fourier spectral
method is employed in space when the periodic boundary conditions are
specified. Some numerical experiments on the Allen-Cahn, Cahn-Hilliard, and
phase field crystal models are conducted to validate those theories as well as
the effectiveness, the energy stability and the accuracy of our schemes.
