  The noise decoupling problem is investigated for general N-level Markovian
open quantum systems. Firstly, the concept of Cartan decomposition of the Lie
algebra $su(N)$ is introduced as a tool of designing control Hamiltonians.
Next, under certain assumptions, it is shown that a part of variables of the
coherence vector of the system density matrix can be asymptotically decoupled
from the environmental noises. The resulting noise decoupling scheme is applied
to one-qubit, qutrit and two-qubit quantum systems, by which the coherence
evolution of the one-qubit and qutrit systems can always be asymptotically
preserved, while, for two-qubit systems, our findings indicate that evolution
of some variables can be preserved only for some initial states.
