  As a hybrid of techniques from open-loop and feedback control, Lyapunov
control has the advantage that it is free from the measurement-induced
decoherence but it includes the system's instantaneous message in the control
loop. Often, the Lyapunov control is confronted with time delay in the control
fields and difficulty in practical implementations of the control. In this
paper, we study the effect of time-delay on the Lyapunov control, and explore
the possibility of replacing the control field with a pulse train or a
bang-bang signal. The efficiency of the Lyapunov control is also presented
through examining the convergence time of the controlled system. These results
suggest that the Lyapunov control is robust gainst time delay, easy to realize
and effective for high-dimensional quantum systems.
