This paper shows that fundamental limitations arise from the presence of stable zeros on or near the j omega-axis. The stability of the closed-loop system is used in conjunction with the Laplace transform to show that time domain integral constraints must be satisfied by the system response. The presence of stable zeros near the j omega axis together with upper limits on the permissible overshoot of the output signal, place an effective lower bound on the settling time of the closed loop system. The constraints are illustrated by an application to the control of a single stand reversing mill.