Stability of discrete-time feed-forward neural networks in NARX configuration

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