# Converse Theorems for Safety and Barrier Certificates

arXiv: https://arxiv.org/abs/1701.03948 · HTML: https://mlsanity.com/paper/1701.03948/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2017.

## Built on by (most cited first, 1 of 1)

- [A General Framework for Verification and Control of Dynamical Models via Certificate Synthesis](https://mlsanity.com/paper/2309.06090/) (2023)

## Abstract (arXiv)

An important tool for proving safety of dynamical systems is the notion of a barrier certificate. In this paper we prove that every robustly safe ordinary differential equation has a barrier certificate. Moreover, we show a construction of such a barrier certificate based on a set of states that is reachable in finite time.