Global stabilization for nonlinear uncertain systems with unmodeled actuator dynamics

Recently developed, second-order sliding-mode control (2-SMC) algorithms ar e analyzed to assess their global convergence properties. While standard fi rst-order sliding-mode control (I-SMC) algorithms derive their effectivenes s from the global solution of the well known "reaching condition" s(s)over dot less than or equal to -k(2) \s \ (s = 0 being the actual sliding manifo ld), 2-SMC is based on more complex differential inequalities, for which a global solution could not exist. The approach presented in this note introd uces a suitable commutation logic (based on an online simple predictor) tha t prevents an uncontrollable growth of the uncertainties. Thanks to this ne w commutation logic, the global convergence of the state trajectory to the designed sliding manifold is ensured.