  We present a scheme to drive a finite-dimensional quantum system into the
decoherence-free subspaces(DFS) by Lyapunov control. Control fields are
established by Lyapunov function. This proposal works well for both closed and
open quantum systems, with replacing the DFS by desired subspaces for closed
systems. An example which consists of a four-level system with three degenerate
states driven by three lasers is presented to gain further insight of the
scheme, numerical simulations for the dynamics of the system are performed and
the results are good.

Quantum Physics