A sensitivity tradeoff for plants with time delay

In this paper we show that the sensitivity function of a scalar feedback system must satisfy an integral constraint when the open-loop transfer function is strictly proper and contains a time delay. The integral constraint is identical to the classical Bode sensitivity integral, which holds provided the open-loop gain has greater than a one-pole rolloff. The design implications of the two constraints are somewhat different, however, and this difference is discussed. The relation between open-loop phase and a conflict between bandwidth and sensitivity properties is explored.