Multi-input sliding mode control of a class of uncertain nonlinear systems

An effective way to extend to the multi-input case the variable structure control philosophy is based on a set of m +1 control vectors forming a simplex in Rm and on the corresponding switching of the controlled system from one to another of m +1different structures. Yet, some problems arise when uncertainties are present in certain matrices characterizing the controlled systems. In this paper, conditions are identified under which, even in the presence of uncertainty, the convergence to the sliding manifold is ensured via the application of a multi-input control strategy still based on a simplex of control vectors.