The solution of the invariance problem for arbitrary external perturbations is proposed for the system output control. It is assumed that perturbations are not measured, and acts through another channels than control inputs (so called unmatched perturbation). The nonlinear control algorithms are developed on the base of discontinuous function. The main idea consists in using relay linearization effect with the help of self damping oscillations of the system output. In such operation mode the theoretically infinite linearization coefficient can be realized, and asymptotical invariance of the system output is provided. The simulation results show the effciency of the designed algorithms.