Multi-input sliding mode control of uncertain nonlinear systems through simplex methods

In this chapter a multi-input sliding mode control technique, called the simplex method, is presented. Multi-input sliding mode control for nonlinear uncertain systems is far from simply being a generalization of the standard single input variable structure control (VSC) approach, except for the case in which the uncertainties, though affecting the system model, do not appear in the control matrix, and this latter is invertible. In the case in which the control matrix is uncertain, some structural properties need to be guaranteed in order to be able to design a sliding mode control vector [l], [2].