  We explore set-stabilizability by constrained controls, and both
controllability and stabilizability can be regarded as the special case of
set-stabilizability. We not only clarify how to define an equilibrium point of
Schr$\ddot{o}$dinger Equations, but also establish the necessary and sufficient
conditions for stabilizability of quantum systems. Unfortunately, it is
revealed that the necessary conditions are quite strict for stabilizability of
some concrete quantum systems like nuclear spin systems, and this further
justifies the introduction of set-stabilizability notion. It is also
exemplified that set-stabilizability can be used for investigating quantum
information processing problems including quantum information storage and
entangled states generation.
