We study the local stability of nonlinear systems in the Luré 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.
View on arXiv@article{hedesh2025_2505.22889,
title={ Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints },
author={ Hamidreza Montazeri Hedesh and Moh Kamalul Wafi and Milad Siami },
journal={arXiv preprint arXiv:2505.22889},
year={ 2025 }
}