Regions of Attraction of CBF-Based Safety Filters for Stable Planar Linear Systems
This study investigates how safety filters, based on control barrier functions (CBFs), affect the dynamics of a simple planar linear system with an affine constraint. It shows that even in this basic setting, the filtered system can oscillate or diverge while remaining safe. The research fully characterizes conditions for global stability and identifies how the filter creates saddle points on constraint boundaries.