# Learning Stable and Robust Linear Parameter-Varying State-Space Models

arXiv: https://arxiv.org/abs/2304.01828 · HTML: https://mlsanity.com/paper/2304.01828/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Stable Recurrent Models](https://mlsanity.com/paper/1805.10369/) (2018)
- [Direct Parameterization of Lipschitz-Bounded Deep Networks](https://mlsanity.com/paper/2301.11526/) (2023)
- [Lipschitz Bounded Equilibrium Networks](https://mlsanity.com/paper/2010.01732/) (2020)
- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramian](https://mlsanity.com/paper/2303.11835/) (2023)
- [Deep-Learning-Based Identification of LPV Models for Nonlinear Systems](https://mlsanity.com/paper/2204.04060/) (2022)
- [Convex Incremental Dissipativity Analysis of Nonlinear Systems - Extended version](https://mlsanity.com/paper/2006.14201/) (2020)
- [LPVcore: MATLAB Toolbox for LPV Modelling, Identification and Control](https://mlsanity.com/paper/2105.03695/) (2021)
- [Linear Parameter-Varying Subspace Identification: A Unified Framework](https://mlsanity.com/paper/2008.03347/) (2020)

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

- [PAC bounds of continuous Linear Parameter-Varying systems related to neural ODEs](https://mlsanity.com/paper/2307.03630/) (2023)

## Abstract (arXiv)

This paper presents two direct parameterizations of stable and robust linear parameter-varying state-space (LPV-SS) models. The model parametrizations guarantee a priori that for all parameter values during training, the allowed models are stable in the contraction sense or have their Lipschitz constant bounded by a user-defined value γ. Furthermore, since the parametrizations are direct, the models can be trained using unconstrained optimization. The fact that the trained models are of the LPV-SS class makes them useful for, e.g., further convex analysis or controller design. The effectiveness of the approach is demonstrated on an LPV identification problem.