First and second order sliding mode stabilizing controller for a perturbed regular form

Deals with the perturbation effects on the generalized regular form and its stabilization using first and second order sliding mode controllers. First, it is shown that if the perturbation belongs to a particular geometric distribution then it only appears in the "controlled" part of the generalized regular form. The classical matching condition obtained by Drazenovic (1969) can be recovered by this result. The last part is devoted to the stabilization problem in presence of perturbations with known bounds: a first and a second order SMC are proposed.