Hybrid Lyapunov and Barrier Function-Based Control with Stabilization Guarantees

Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs) can be combined, typically by means of Quadratic Programs (QPs), to design controllers that achieve performance and safety objectives. However, a significant limitation of this framework is the introduction of asymptotically stable equilibrium points besides the minimizer of the CLF, leading to deadlock situations even for simple systems and bounded convex unsafe sets. To address this problem, we propose a hybrid CLF-CBF control framework with global asymptotic stabilization and safety guarantees, offering a more flexible and systematic design methodology compared to current alternatives available in the literature. We further extend this framework to higher-order systems via a recursive procedure based on a joint CLF-CBF backstepping approach. The proposed solution is assessed through several simulation examples.