Learning the dynamics of nonlinear systems with regional stability guarantees through linear matrix inequality constraints
Abstract
This paper presents a method that learns a regionally stable recurrent neural network model from a set of input-output data generated by an unknown dynamical system. Relying on generalized sector conditions on the deadzone activation function, we first derive sufficient conditions that guarantee forward invariance on a compact set of the state space for any inputs from a given set. Such regional properties lead to less conservative conditions compared to variants that offer a global form of stability, and are in line with the system data that is only observed regionally. Our learning method derives conditions for regional stability using a barrier function approach, leading to models equipped with a certificate of regional stability in a subset of the state space and for a given input set. We illustrate our theoretical result with a numerical example and compare it to methods that impose a global form of stability, which fail to identify the system, and with a method that imposes no stability constraints at all, which does not guarantee a stable behavior within any state or input set.
Keywords
Cite
@article{arxiv.2605.18292,
title = {Learning the dynamics of nonlinear systems with regional stability guarantees through linear matrix inequality constraints},
author = {Daniel Frank and Fahim Shakib and Steffen Staab},
journal= {arXiv preprint arXiv:2605.18292},
year = {2026}
}
Comments
This work has been accepted to IFAC for publication under a Creative Commons Licence CC-BY-NC-ND