Integrator backstepping for uncertain nonlinear systems with non-smooth dynamics

We solve the problem of global input-to-state stabilization with respect to external disturbances for a class of nonlinear systems with unknown parameters. For this class, the classical backstepping framework is not applicable and needs to be redesigned because of the following obstacles: (a) the systems under consideration are not in strict-feedback form, are not feedback linearizable and their input-output maps are not invertible, and (b) the dynamics is non-smooth and the trajectories starting from an initial point are not necessarily uniquely defined.