Generalized Sliding-Mode Control for Multi-Input Nonlinear Systems

The purpose of this paper is to present a framework for the design of sliding-mode based controllers for multi-input affine nonlinear systems. In this framework the control effort goes to zero as the state approaches the sliding surface, a key feature for practical implementation. The sliding surface is a submanifold with codimension equal to the dimension of the involutive distribution G generated by the controlled vector fields rather than the dimension of their linear span. We also allow nonzero vectors in G to be tangent to the sliding surface, the singular case in sliding-mode control