Global stabilization for nonlinear uncertain systems with unmodeled actuator dynamics

Recently developed, second-order sliding-mode control (2-SMC) algorithms are analyzed to assess their global convergence properties. While standard first-order sliding-mode control (1-SMC) algorithms derive their effectiveness from the global solution of the well known “reaching condition” _ ( = 0 being the actual sliding manifold), 2-SMC is based on more complex differential inequalities, for which a global solution could not exist. The approach presented in this note introduces a suitable commutation logic (based on an online simple predictor) that prevents an uncontrollable growth of the uncertainties. Thanks to this new commutation logic, the global convergence of the state trajectory to the designed sliding manifold is ensured.