Learning the dynamics of nonlinear systems with regional stability guarantees through linear matrix inequality constraints

Daniel Frank; Fahim Shakib; Steffen Staab

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arXiv · 2605.18292

Learning the dynamics of nonlinear systems with regional stability guarantees through linear matrix inequality constraints

Daniel Frank·Fahim Shakib·Steffen Staab

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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.

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BibTeX RIS

Daniel Frank, Fahim Shakib, Steffen Staab. 2026-05-18. Learning the dynamics of nonlinear systems with regional stability guarantees through linear matrix inequality constraints. https://arxiv.org/abs/2605.18292

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