The usual design problem is to determine a control signal sequence which operates on a plant to meet certain prescribed design specifications or performance criteria. The concept of controllability and observability play an important role in time-optimal control systems. In most of the cases, although the problem is given in the frequency domain, it is usual to convert it into the time domain for determining the optimal control sequence. It is shown in this paper that such a procedure is unnecessary and that the entire design for time-optimal performance can be carried out in the frequency domain itself.