Designing r-sliding mode control using smooth iterative manifolds

In this paper we discuss some specific issues related to higher order sliding mode control design. We highlight the efficiency of such control design with respect to finite time convergence and robustness in the case where the system possesses a relative degree greater than one. We also point out some difficulties that arise due to the fact that eventually some derivative terms becomes very large. In addition, we also propose a smooth sliding manifold for the case where the system possesses a relative degree greater than one. The problem of practical finite-time stability is also discussed. Finally, we present an illustrative example for third order sliding mode.