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Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints
Hamidreza Montazeri Hedesh, Moh Kamalul Wafi, Milad Siami
https://arxiv.org/abs/2505.22889

Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints
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 a…