Continuous-time performance limitations for overshoot and resulted tracking measures

A dual formulation for the problem of determining absolute performance limitations on overshoot, undershoot, maximum amplitude and fluctuation minimisation for continuous-time feedback systems is constructed. Determining , for example, the minimum possible overshoot attainable by all possible stabilising controllers is an optimisation task that cannot be expressed as a minimum-norm problem. It is this fact, coupled with the continuous-time rather than discrete-time formulation, that makes these problems challenging. We extend previous results to include more general reference functions, and derive new results (in continuous time) on the influence of pole/zero locations on achievable time-domain performance.