arXiv:2610.30545v1 Announce Type: new Abstract: This paper presents a novel approach for the construction of control barrier functions (CBFs) for controllable linear systems subject to multiple state and input constraints. The approach is based on the Dynamic Backup CBF (DB-CBF) framework, where the control policy is parametrized using the equilibrium subspace of the system. By using a minimum-energy finite-time controller, we show that the terminal set constraint trivially reduces to having an admissible equilibrium point. The proposed DB-CBF is easy to tune (one parameter), fully takes advantage of the input range (by minimizing the control effort), and guarantees constraint enforcement (by tracking a backup equilibrium point that can be reached safely in finite time).