A general class of sliding surface for sliding mode control

In the conventional sliding mode control, the relative degree of the chosen sliding surface is usually one. This paper addresses a general class of sliding surface whose relative degree is no longer restricted to one. We show that when the relative degree is more than two, it is inevitable that there will exist a limit cycle for the nonlinear sign function. For the case of relative degree two, the system possesses poor phase margin. However, these disadvantages can be overcome by soothing out the control nonlinearity in a suitable boundary layer with a saturation function that ensures globally exponential stability of the overall system.