Safe Stabilization Using Non‐Smooth Control Lyapunov Barrier Function

ABSTRACT This paper addresses the challenge of safe stabilization, ensuring the system state reaches the origin while avoiding unsafe state regions. Existing approaches that rely on smooth Lyapunov barrier functions often fail to guarantee a feasible controller. To overcome this limitation, we introduce the non‐smooth control Lyapunov barrier function (NCLBF), which ensures the existence of a safe and stabilizing controller. We provide a systematic framework for designing NCLBF and feedback control strategies to achieve safe stabilization in the presence of multiple bounded unsafe regions. Theoretical analysis and simulations of both linear and nonlinear systems demonstrate the effectiveness and superiority of our approach compared to the existing smooth functions method.