The problem of compensating for external disturbances is one of the oldest problems in the classical theory of control. The article considers the task of stabilizing the output variable under the influence of external non-smooth disturbances, that do not belong to the control space. A discontinuous control law has been developed to provide a prescribed control accuracy for the output. Various variants of the transient process in the closed loop system are described, estimates of overshooting and steady-state error are given. The proposed approach can be widely used to compensate the bounded external disturbances, including those, that depend on the state of the system.