# Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification

arXiv: https://arxiv.org/abs/2510.24757 · HTML: https://mlsanity.com/paper/2510.24757/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Continuous-time system identification with neural networks: Model structures and fitting criteria](https://mlsanity.com/paper/2006.02915/) (2020)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)
- [Enhancing Continuous Time Series Modelling with a Latent ODE-LSTM Approach](https://mlsanity.com/paper/2307.05126/) (2023)
- [SIMBa: System Identification Methods leveraging Backpropagation](https://mlsanity.com/paper/2311.13889/) (2023)
- [Deep Learning of Dynamic Systems using System Identification Toolbox(TM)](https://mlsanity.com/paper/2409.07642/) (2024)
- [Stable Linear Subspace Identification: A Machine Learning Approach](https://mlsanity.com/paper/2311.03197/) (2023)
- [dynoGP: Deep Gaussian Processes for dynamic system identification](https://mlsanity.com/paper/2502.05620/) (2025)
- [Introducing Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2504.18845/) (2025)

## Built on by (most cited first, 2 of 2)

- [SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems](https://mlsanity.com/paper/2604.14879/) (2026)
- [Explainable Wastewater Digital Twins: Adaptive Context-Conditioned Structured Simulators with Self-Falsifying Decision Support](https://mlsanity.com/paper/2605.19826/) (2026)

## Abstract (arXiv)

Accurate modeling of nonlinear systems is essential for reliable control, yet conventional identification methods often struggle to capture latent dynamics while maintaining stability. We propose a textitstable-by-design LPV neural network-based state-space (NN-SS) model that simultaneously learns latent states and internal scheduling variables directly from data. The state-transition matrix, generated by a neural network using the learned scheduling variables, is guaranteed to be stable through a Schur-based parameterization. The architecture combines an encoder for initial state estimation with a state-space representer network that constructs the full set of scheduling-dependent system matrices. For training the NN-SS, we develop a framework that integrates multi-step prediction losses with a state-consistency regularization term, ensuring robustness against drift and improving long-horizon prediction accuracy. The proposed NN-SS is evaluated on benchmark nonlinear systems, and the results demonstrate that the model consistently matches or surpasses classical subspace identification methods and recent gradient-based approaches. These findings highlight the potential of stability-constrained neural LPV identification as a scalable and reliable framework for modeling complex nonlinear systems.