  Linearized complex Ginzburg-Landau equation models various physical phenomena
and the stability controls of them are important. In this paper, we study the
control of the LCGLE with a simultaneously space and time dependent coefficient
by transforming it into a complex heat equation. It is shown that under certain
conditions on the coefficient functions $a_2(\tilde{x},\tilde{t})$, the
exponential stability of the system at any rate can be achieved by boundary
control based on the state feedback. The kernels are {\it explicitly}
calculated as series of approximation and shown to be twice differentiable by
using the {\it method of dominant}. Both the exponential stabilities of the
systems with Dirichlet and Neumann boundary conditions are strictly proven.
