Fundamental limitations on the time-domain shaping of response to a fixed input

In this paper, we examine time-domain limitation-of-performance problems in feedback control system design. The main result is a theorem which gives a dual formulation to the problem of determining absolute limits on the time-domain shaping of the response to a fixed input. The duals that arise are particularly illuminating. They have a simple interpretation as optimizing the impulse response of a transfer function whose poles are readily constructed from the data. Much insight is obtainable from the dual, for example, in helping to classify classes of plants with the same quantitative behavior. New results on classical performance measures, such as overshoot and undershoot, are presented. We also examine minimization of the difference between the maximum and minimum values of the error response, a quantity we term fluctuation.