A novel adaptive sliding mode controller is proposed for a class of nonlinear MIMO systems with bounded uncertainties/perturbations whose bounds are unknown. The adaptation algorithm ensures that the gain is not overestimated, which leads to a reduction of chattering; furthermore, the controller ensures the establishment of a real sliding mode (which induces the practical stability of the closed-loop system). The algorithm is applied to position-pressure control of an electropneumatic actuator. The results of the experimental study are presented and confirmed the efficacy of the proposed adaptive sliding mode control.