The new second order sliding mode algorithm and convergence proof

One of the algorithms of the second order sliding mode is considered under the action of external bounded and smooth disturbances. A distinctive feature of the proposed feedback is that the differential equation of the closed system is not homogeneous. A final proof of convergence for such systems is given under assumption that the disturbances are acting in the control channels only. By using the new algorithm control system was made able to give the final convergence property by using a lower control resources.