On the stability of nonlinear sampled-data systems and their continuous-time limits

TL;DR

This paper investigates the stability of nonlinear sampled-data systems with nonuniform sampling and establishes links between their discrete-time models and continuous-time limits, enabling easier stability analysis.

Contribution

It introduces new relationships between the stability of exact discrete models and continuous-time systems as sampling periods approach zero, improving stability guarantees for nonlinear systems.

Findings

Allows inference of sampled-data stability from continuous-time stability

Proves stronger asymptotic stability results for nonlinear systems

Extends stability analysis to nonuniform sampling scenarios

Abstract

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic) sampling instants and the stability property of the continuous-time system when the maximum admissible sampling period converges to zero. These results can be used to infer stability properties for the sampled-data system by direct inspection of the stability of the mentioned continuous-time system, a task which is typically easier than the analysis of the closed-loop sampled-data system. Compared to the literature, our results allow to prove stronger (asymptotic) sampled-data stability properties for nonlinear systems in cases for which existing results only guarantee practical stability.