On multi-input second order sliding mode control of nonlinear systems with uncertainty

Some works presented in the literature have shown the effectiveness of second order sliding modes (i.e. a sliding regime on a set s(x(t))=s˙(x(t))=0 enforced by a control signal directly acting on s¨(t)) in controlling uncertain systems. Such an approach, in its native formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In this paper the validity of a second order sliding mode control algorithm, previously presented by the authors (1997, 1999), is extended to some classes of multi-input nonlinear uncertain systems, covering a wide class of real processes. The chattering avoidance feature of the proposed second order sliding mode control scheme is presented as an example for a class of multi-input systems