This paper presents a new dynamic integral quadratic constraint (IQC) for the repeated Rectified Linear Unit (ReLU). These dynamic IQCs can be used to analyze stability and induced ℓ2-gain performance of discrete-time, recurrent neural networks (RNNs) with ReLU activation functions. These analysis conditions can be incorporated into learning-based controller synthesis methods, which currently rely on static IQCs. We show that our proposed dynamic IQCs for repeated ReLU form a superset of the dynamic IQCs for repeated, slope-restricted nonlinearities. We also prove that the ℓ2-gain bounds are nonincreasing with respect to the horizon used in the dynamic IQC filter. A numerical example using a simple (academic) RNN shows that our proposed IQCs lead to less conservative bounds than existing IQCs.
Cite
@article{arxiv.2603.17137,
title = {Integral Quadratic Constraints for Repeated ReLU},
author = {Sahel Vahedi Noori and Bin Hu and Geir Dullerud and Peter Seiler},
journal= {arXiv preprint arXiv:2603.17137},
year = {2026}
}