Ballaben, RiccardoBraun, PhilippZaccarian, Luca2026-06-112026-06-112475-1456ORCID:/0000-0002-9619-1483/work/217150128https://hdl.handle.net/1885/733810658For control-affine nonlinear systems, we augment a predefined Lyapunov-based global stabilizer with a hybrid obstacle avoidance design preserving the Lyapunov decrease. While the method can be applied to the general class of control-affine systems, the size of the avoidance neighborhood is not a design parameter. Our design shows that a system can achieve global asymptotic stability with simultaneous unsafe set avoidance via hybrid feedback, which overcomes well-known issues of topological obstructions.6enPublisher Copyright: © 2017 IEEE.constrained controlLyapunov methodsstability of hybrid systems202410.1109/LCSYS.2024.340477085194029437