Abstract

It is shown that every asymptotically stable, strictly proper, type m continuous time scalar system tracks every polynomial trajectory of up to order m - 2, with an instantaneous tracking error whose integral over the interval [0, + infinity) identically vanishes. This determines that the system will always exhibit overshoot in each of the above responses. This phenomenon constitutes an essential manifestation of the existing trade-off between steady state and transient accuracies.