Adaptive composite non-linear feedback-based sliding mode control for non-linear systems

An adaptive composite non-linear feedback based sliding mode controller is proposed for a class of non-linear systems comprising uncertainty terms. In these cases, it is theoretically proved that the trajectory of the closed-loop system converges to the sliding surface in a finite-time manner. Also, by the means of numerical linear matrix inequality technique, the stability of the non-linear system along the sliding surface is turned to an linear matrix inequality problem. By solving such problem, the unknown matrix of the sliding surface and composite non-linear feedback based sliding mode controller is obtained. Finally, to show the merits of the proposed approach, it is applied to practical non-linear DC servomotor.