Constructing a Generalized Lyapunov Barrier Function for Safe Stabilization of Nonlinear Control Systems

This paper introduces the concept of a generalized (nonsmooth) Lyapunov barrier function (GenLBF) to unify control Lyapunov function (CLF) and control barrier function (CBF) for certifying KL-stability and safety of nonlinear control systems. The authors propose a systematic approach for constructing a suitable GenLBF and an efficient method for evaluating its generalized derivative. The GenLBF-based control design ensures safe stabilization of both autonomous and non-autonomous systems.