  A scheme to drive and manipulate a finite-dimensional quantum system in the
decoherence-free subspaces(DFS) by Lyapunov control is proposed. Control fields
are established by Lyapunov function. This proposal can drive the open quantum
system into the DFS and manipulate it to any desired eigenstate of the free
Hamiltonian. An example which consists of a four-level system with three
long-lived states driven by two lasers is presented to exemplify the scheme. We
have performed numerical simulations for the dynamics of the four-level system,
which show that the scheme works good.
