Differential geometric methods in variable-structure control

This article presents a differential geometric approach for the design of sliding modes in non-linear variable-structure feedback systems. Coordinate-free characterizations of local existence conditions for sliding regimes, and a geometric reformulation of some of its most salient features are presented. The approach uses basic notions from differential geometry involving vector fields, distributions and 1-forms. Both single- and multiple-input cases are treated with some illustrative examples.