  Sampling in control applications is increasingly done non-equidistantly in
time. This includes applications in motion control, networked control,
resource-aware control, and event-based control. Some of these applications,
like the ones where displacement is tracked using incremental encoders, are
driven by signals that are only measured when their values cross fixed
thresholds in the amplitude domain. This paper introduces a non-parametric
estimator of the impulse response and transfer function of continuous-time
systems based on such amplitude-equidistant sampling strategy, known as
Lebesgue sampling. To this end, kernel methods are developed to formulate an
algorithm that adequately takes into account the bounded output uncertainty
between the event timestamps, which ultimately leads to more accurate models
and more efficient output sampling compared to the equidistantly-sampled
kernel-based approach. The efficacy of our proposed method is demonstrated
through a mass-spring damper example with encoder measurements and extensive
Monte Carlo simulation studies on system benchmarks.
