  As a key method in dealing with uncertainties, feedback has been understood
fairly well in classical control theory. But for quantum control systems, the
capability of measurement-based feedback control (MFC) has not been
investigated systematically. In contrast to the control of classical systems
where the measurement effect is negligible, the quantum measurement will cause
a quantum state to collapse, which will inevitably introduce additional
uncertainties besides the system initial uncertainty. Therefore, there is a
complicated tradeoff between the uncertainty introduced and the information
gained by the measurement, and thus a theoretical investigation of the
capability of MFC is of fundamental importance. In this paper, inspired by both
the Heisenberg uncertainty principle for quantum systems and the investigation
of the feedback capability for classical systems, we try to answer the
following three basic questions: (i) How to choose the measurement channel
appropriately? (ii) Is the MFC still superior to the open loop control in
dealing with the system information uncertainties? and (iii) What is the
maximum capability or limitation of the MFC? These questions will be answered
theoretically by establishing several theorems concerning the asymptotic
reachability of eigenstates of a typical class of Hamiltonian control mode.
