# Control Barrier Functions in Sampled-Data Systems

arXiv: https://arxiv.org/abs/2103.03677 · HTML: https://mlsanity.com/paper/2103.03677/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2021.

## Built on by (most cited first, 6 of 6)

- [CBF-RL: Safety Filtering Reinforcement Learning in Training with Control Barrier Functions](https://mlsanity.com/paper/2510.14959/) (2025)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Meta-Reinforcement Learning for Robust and Non-greedy Control Barrier Functions in Spacecraft Proximity Operations](https://mlsanity.com/paper/2602.07335/) (2026)
- [PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles](https://mlsanity.com/paper/2511.15522/) (2025)
- [Memory-Efficient Meta-Reinforcement Learning for Adaptive Safety-Critical Control in Adversarial Spacecraft Proximity Operations](https://mlsanity.com/paper/2606.17414/) (2026)

## Abstract (arXiv)

This paper presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the conservativeness of sufficient conditions on forward invariance under piecewise-constant controllers. Then, we propose three approaches for guaranteeing forward invariance, two motivated by continuous-time barrier functions, and one motivated by discrete-time barrier functions. All proposed conditions are control affine, and thus can be incorporated into quadratic programs for control synthesis. We show that the proposed conditions are less conservative than those in earlier studies, and show via simulation how this enables the use of barrier functions that are impossible to implement with the desired time-step using existing methods.