# Delay Independent Safe Control with Neural Networks: Positive Lur'e Certificates for Risk Aware Autonomy

arXiv: https://arxiv.org/abs/2510.06661 · HTML: https://mlsanity.com/paper/2510.06661/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 14 of 14)

- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks](https://mlsanity.com/paper/1708.03322/) (2017)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers](https://mlsanity.com/paper/2006.07579/) (2020)
- [Can Transformers Learn Optimal Filtering for Unknown Systems?](https://mlsanity.com/paper/2308.08536/) (2023)
- [Efficient Reachability Analysis of Closed-Loop Systems with Neural Network Controllers](https://mlsanity.com/paper/2101.01815/) (2021)
- [Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllers](https://mlsanity.com/paper/2406.12744/) (2024)
- [Convex Data-Driven Contraction With Riemannian Metrics](https://mlsanity.com/paper/2412.20283/) (2024)
- [QSID-MPC: Model Predictive Control with System Identification from Quantized Data](https://mlsanity.com/paper/2503.19102/) (2025)
- [Robust Stability Analysis of Positive Lure System with Neural Network Feedback](https://mlsanity.com/paper/2505.18912/) (2025)
- [Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints](https://mlsanity.com/paper/2505.22889/) (2025)
- [Koopman Meets Limited Bandwidth: Effect of Quantization on Data-Driven Linear Prediction and Control of Nonlinear Systems](https://mlsanity.com/paper/2501.07714/) (2025)

## Abstract (arXiv)

We present a risk-aware safety certification method for autonomous, learning enabled control systems. Focusing on two realistic risks, state/input delays and interval matrix uncertainty, we model the neural network (NN) controller with local sector bounds and exploit positivity structure to derive linear, delay-independent certificates that guarantee local exponential stability across admissible uncertainties. To benchmark performance, we adopt and implement a state-of-the-art IQC NN verification pipeline. On representative cases, our positivity-based tests run orders of magnitude faster than SDP-based IQC while certifying regimes the latter cannot-providing scalable safety guarantees that complement risk-aware control.