  The aim of this work is to investigate the use of Incrementally
Input-to-State Stable ($\delta$ISS) deep Long Short Term Memory networks
(LSTMs) for the identification of nonlinear dynamical systems. We show that
suitable sufficient conditions on the weights of the network can be leveraged
to setup a training procedure able to learn provenly-$\delta$ISS LSTM models
from data. The proposed approach is tested on a real brake-by-wire apparatus to
identify a model of the system from input-output experimentally collected data.
Results show satisfactory modeling performances.
