Discrete sliding mode control for systems with arbitrary relative degree output

The paper presents an analysis of sliding mode control of discrete time systems with relative degree greater than one. The analysis leads us to obtain finite time stability of the output as well as the states of the system in absence of uncertainties, taking the output as the sliding variable. The simple equivalent control with state feedback guarantees this. In presence of uncertainties in the system model, the states and the output are ultimately bounded if the uncertainties are bounded in nature. It is also shown in the latter case, that the robustness of the output can be increased when the relative degree is more than one.