H₂ Tracking Performance Limitation in Sampled-Data Feedback Control

Abstract

In this paper we investigate the best achievable H₂ tracking performance for a step reference signal using sampled-data control systems. We derive an analytical closed form expression for the optimal tracking performance, which consists of the following three parts: the nonminimum phase zeros of the continuous-time plant, the non-minimum phase zeros of the discretized plant/antialiasing filter due to sampling, and the aliasing effects of sideband harmonics.