# Deep Long-Short Term Memory networks: Stability properties and Experimental validation

arXiv: https://arxiv.org/abs/2304.02975 · HTML: https://mlsanity.com/paper/2304.02975/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Multi-Step Prediction of Dynamic Systems with Recurrent Neural Networks](https://mlsanity.com/paper/1806.00526/) (2018)
- [On the stability properties of Gated Recurrent Units neural networks](https://mlsanity.com/paper/2011.06806/) (2020)
- [On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments](https://mlsanity.com/paper/2111.13557/) (2021)
- [LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification](https://mlsanity.com/paper/1912.04377/) (2019)
- [An overview and comparative analysis of Recurrent Neural Networks for Short Term Load Forecasting](https://mlsanity.com/paper/1705.04378/) (2017)
- [Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networks](https://mlsanity.com/paper/2103.02383/) (2021)
- [Recurrent Neural Network-based Model Predictive Control for Continuous Pharmaceutical Manufacturing](https://mlsanity.com/paper/1807.09556/) (2018)
- [Stability of discrete-time feed-forward neural networks in NARX configuration](https://mlsanity.com/paper/2012.03741/) (2020)
- [Recurrent Neural Network-based Internal Model Control design for stable nonlinear systems](https://mlsanity.com/paper/2108.04585/) (2021)
- [An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX models](https://mlsanity.com/paper/2203.16290/) (2022)

## Built on by (most cited first, 1 of 1)

- [Enhancing AI System Resiliency: Formulation and Guarantee for LSTM Resilience Based on Control Theory](https://mlsanity.com/paper/2505.17696/) (2025)

## Abstract (arXiv)

The aim of this work is to investigate the use of Incrementally Input-to-State Stable (δISS) 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-δISS 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.