  We propose an algorithmic approach for synthesizing linear hybrid automata
from time-series data. Unlike existing approaches, our approach provides a
whole family of models. Each model in the family is guaranteed to capture the
input data up to a precision error {\epsilon}, in the following sense: For each
time series, the model contains an execution that is {\epsilon}-close to the
data points. Our construction allows to effectively choose a model from this
family with minimal precision error {\epsilon}. We demonstrate the algorithm's
efficiency and its ability to find precise models in two case studies.
