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arXiv · 2505.22889

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

Hamidreza Montazeri Hedesh·Moh Kamalul Wafi·Milad Siami
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Abstract

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.

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Hamidreza Montazeri Hedesh, Moh Kamalul Wafi, Milad Siami. 2025-10-03. Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints. https://arxiv.org/abs/2505.22889

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