Existence of alternative safe subset function constructions

Determine whether safe subset functions for disjunctive safe sets admit constructions other than projection onto convex components of the unsafe set and the eigenvector-selection function defined in equation (20).

Background

The paper studies subset-based discrete-time exponential matrix control barrier functions for safe sets that are unions of convex sets. Prior work constructs safe subset functions by projecting onto convex components of the unsafe set and forming separating hyperplanes, whereas the present paper introduces an eigenvector-based construction that avoids projection. The authors explicitly identify the existence of further constructions as unresolved.

References

In [21], safe subset functions are constructed by projection onto convex components of the unsafe set, and the question of whether other constructions exist is left open.

— Convex Safety Filtering via Spectral Selection for Nonconvex Safe Sets  (2610.12324 - Salazar et al., 8 Oct 2026) in Remark 3, Section IV.B (PDF page 5)