  Studied in this article is non-Markovian open quantum systems parametrized by
Hamiltonian H, coupling operator L, and memory kernel function {\gamma}, which
is a proper candidate for describing the dynamics of various solid-state
quantum information processing devices. We look into the subspace stabilization
problem of the system from the perspective of dynamical systems and control.
The problem translates itself into finding analytic conditions that
characterize invariant and attractive subspaces. Necessary and sufficient
conditions are found for subspace invariance based on algebraic computations,
and sufficient conditions are derived for subspace attractivity by applying a
double integral Lyapunov functional. Mathematical proof is given for those
conditions and a numerical example is provided to illustrate the theoretical
result.
