  The idea of using Feed-Forward Neural Networks (FFNNs) as regression
functions for Nonlinear AutoRegressive eXogenous (NARX) models, leading to
models herein named Neural NARXs (NNARXs), has been quite popular in the early
days of machine learning applied to nonlinear system identification, owing to
their simple structure and ease of application to control design. Nonetheless,
few theoretical results are available concerning the stability properties of
these models. In this paper we address this problem, providing a sufficient
condition under which NNARX models are guaranteed to enjoy the Input-to-State
Stability (ISS) and the Incremental Input-to-State Stability ({\delta}ISS)
properties. This condition, which is an inequality on the weights of the
underlying FFNN, can be enforced during the training procedure to ensure the
stability of the model. The proposed model, along with this stability
condition, are tested on the pH neutralization process benchmark, showing
satisfactory results.
