Controlling output variables via higher order sliding modes

Featuring exactness and robustness, standard sliding mode may also cause the so-called chattering effect. Having hidden the switching in higher derivatives of output variables, higher order sliding modes preserve or generalize the main properties of standard sliding mode and remove the chattering effect. With finite convergence time, the presented controllers provide for full real-time control of the output variable if the relative degree of the dynamic system is known. Used together with recently developed real-time robust exact differentiators, these controllers actually need only measurements of the controlled output variable.