Continuous-time performance limitations for overshoot and resulted tracking measures

TL;DR

This paper develops a dual formulation to determine fundamental limits on overshoot, undershoot, and amplitude in continuous-time feedback systems, highlighting the impact of pole-zero placement on achievable performance.

Contribution

It introduces a dual optimization framework for continuous-time performance limits and extends prior results to more general reference functions and pole-zero configurations.

Findings

Derived new bounds on overshoot and amplitude based on pole-zero locations

Extended previous results to include more general reference functions

Provided insights into how pole-zero placement affects achievable performance

Abstract

A dual formulation for the problem of determining absolute performance limitations on overshoot, undershoot, maximum amplitude and fluctuation minimization for continuous-time feedback systems is constructed. Determining, for example, the minimum possible overshoot attainable by all possible stabilizing controllers is an optimization 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.