Euler Time-Discretization of Funnel-Controlled Dynamics

Thomas Berger, Hannes Gernandt, Pushya Mitra · 2026 · arXiv

DOI: 10.48550/arXiv.2610.27185 · open-access PDF

Abstract

We analyze explicit and implicit Euler discretizations of the continuous-time closed-loop dynamics generated by a funnel controller for a fully actuated nonlinear full-state system of relative degree one with scalar positive input gain. A quantitative continuous-time funnel margin provides the compactness and regularity bounds needed for the error analysis. For explicit Euler, a computable upper step-size threshold guarantees a global nodewise distance from the funnel boundary. We show that first-order convergence holds on finite time horizons and, under a~dissipativity condition (a~one-sided

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