Influence of Zero Locations on the Number of Extrema in the Step Response

Despite the power of modern control techniques, the problem of determining the number of extrema expected in the step response of a transfer function remains open. This note gives an easily computed upper bound for the number of extrema. In several cases this bound is sufficient to determine whether the step response of a closed-loop system will display overshoot. The analysis also permits determining the existence of inverse-response behavior. Criteria helpful in a pole-placement design context are given.