Comparison of Riemann and Lebesgue sampling for first order stochastic systems

TLDR

Digital control traditionally uses periodic (Riemann) sampling, whereas Lebesgue sampling samples only when signals cross predefined thresholds. Lebesgue sampling triggers measurements only when signals exceed specified limits. The study demonstrates that Lebesgue sampling yields superior performance on certain simple systems compared to Riemann sampling.

Abstract

The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.