{"ID":2841136,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.12826","arxiv_id":"2511.12826","title":"Discrete-Time Stability Analysis of ReLU Feedback Systems via Integral Quadratic Constraints","abstract":"This paper analyzes internal stability of a discrete-time feedback system with a ReLU nonlinearity. This feedback system is motivated by recurrent neural networks. We first review existing static quadratic constraints (QCs) for slope-restricted nonlinearities. Next, we derive hard integral quadratic constraints (IQCs) for scalar ReLU by using finite impulse filters and structured matrices. These IQCs are combined with a dissipation inequality leading to an LMI condition that certifies internal stability. We show that our new dynamic IQCs for ReLU are a superset of the well-known Zames-Falb IQCs specified for slope-restricted nonlinearities. Numerical results show that the proposed hard IQCs give less conservative stability margins than Zames-Falb multipliers and prior static QC methods, sometimes dramatically so.","short_abstract":"This paper analyzes internal stability of a discrete-time feedback system with a ReLU nonlinearity. This feedback system is motivated by recurrent neural networks. We first review existing static quadratic constraints (QCs) for slope-restricted nonlinearities. Next, we derive hard integral quadratic constraints (IQCs)...","url_abs":"https://arxiv.org/abs/2511.12826","url_pdf":"https://arxiv.org/pdf/2511.12826v1","authors":"[\"Sahel Vahedi Noori\",\"Bin Hu\",\"Geir Dullerud\",\"Peter Seiler\"]","published":"2025-11-16T23:13:32Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}