When sampling works in data-driven control: Informativity for stabilization in continuous time

TL;DR

This paper develops a framework for understanding when sampled continuous-time signals are informative for system stabilization, introducing new conditions and connecting continuous and discrete control domains.

Contribution

It introduces a novel notion of data informativity for continuous-time stabilization, extending discrete-time results and incorporating noise properties like square Lipschitzness and bounded variation.

Findings

Established conditions for sampled data to be informative for stabilization

Connected continuous and discrete control domains through new assumptions

Validated results with simulations

Abstract

This paper introduces a notion of data informativity for stabilization tailored to continuous-time signals and systems. We establish results comparable to those known for discrete-time systems with sampled data. We justify that additional assumptions on the properties of the noise signals are needed to understand when sampled versions of continuous-time signals are informative for stabilization, thereby introducing the notions of square Lipschitzness and total bounded variation. This allows us to connect the continuous and discrete domains, yielding sufficient conditions to synthesize a stabilizing controller for the true continuous-time system on the basis of sampled data. Simulations illustrate our results.