Relaxed Compatibility Between Control Barrier and Lyapunov Functions

Guaranteeing safety and stability is important in controller design for dynamical systems. Stability can be certified by Control Lyapunov Functions (CLFs), while safety can be certified by Control Barrier Functions (CBFs). These functions constrain the system vector field to certify the corresponding property. However, these constraints may be in conflict with each other at some points. In this paper, we propose a relaxed compatibility condition for a CBF-CLF pair, which can then be used to design a safe and locally stable controller. The proposed concept is demonstrated on a linear system.