Nonlinear variable structure systems in sliding mode: the general case

The problem of inducing local sliding regimes on smooth state-space surfaces of nonlinear single-input-single-output controlled systems is addressed in full generality. The notion of relative degree, in its more general form, is used to establish the most salient features of nonlinear controlled systems undergoing sliding motions, including their characteristic disturbance rejection properties. It is shown that the simplest possible structure at infinity must be exhibited by nonlinear systems undergoing sliding motions on the zero level set of the output feedback function