Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints
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Abstract (arXiv)
We study the local stability of nonlinear systems in the Lur'e form with static nonlinear feedback realized by feedforward neural networks (FFNNs). By leveraging positivity system constraints, we employ a localized variant of the Aizerman conjecture, which provides sufficient conditions for exponential stability of trajectories confined to a compact set. Using this foundation, we develop two distinct methods for estimating the Region of Attraction (ROA): (i) a less conservative Lyapunov-based approach that constructs invariant sublevel sets of a quadratic function satisfying a linear matrix inequality (LMI), and (ii) a novel technique for computing tight local sector bounds for FFNNs via layer-wise propagation of linear relaxations. These bounds are integrated into the localized Aizerman framework to certify local exponential stability. Numerical results demonstrate substantial improvements over existing integral quadratic constraint-based approaches in both ROA size and scalability.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 17 of its 29 references that are in the map. First posted on arXiv 28 May 2025.
Builds on
17 of 29 references.
References · 17
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5 more
- 2024Stability and Performance Analysis of Discrete-Time ReLU Recurrent Neural Networkscited by 4
- 2024Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllerscited by 4
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- 2025Robust Stability Analysis of Positive Lure System with Neural Network Feedbackcited by 2
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Citing papers per year: 2025: 2.
2 papers.