Reaching law based DSMC with higher relative degree sliding variables

Discrete-time sliding variables with relative degree higher than one have been shown to reduce oscillations in switching type quasi-sliding mode strategies and to improve system robustness. In this paper we consider the variables with relative degree equal to the actual degree of the plant. For such variables, a general switching type reaching law is presented. It is demonstrated that the control signal obtained from this reaching law always ensures a finite time response of the closed-loop system. Furthermore, it is shown that our strategy reduces state error compared to the classic relative degree one approach.