This letter studies the dynamical properties of safety filters designed based on Control Barrier Functions (CBF). This mechanism, which is popular in safety-critical applications, takes a nominal controller and minimally modifies it to render it safe. Although CBF-based safety filters make the closed-loop system safe, characterizing their additional dynamical properties, such as stability, boundedness, or existence of spurious equilibria, remains a challenging problem. Here, we address this problem for the case of linear systems and an affine CBF constraint. We provide conditions under which the closed-loop system presents undesired equilibria, unbounded trajectories, or the origin is globally exponentially stable.
@article{arxiv.2603.17401,
title = {Dynamical Properties of Safety Filters for Linear Systems and Affine Control Barrier Functions},
author = {Pol Mestres and Shima Sadat Mousavi and Aaron D. Ames},
journal= {arXiv preprint arXiv:2603.17401},
year = {2026}
}