On multi-input sliding mode control of uncertain nonlinear systems

An effective way to extend to the multi-input case the variable structure control philosophy is that based on a set of m+1 control vectors forming a simplex in ℜ^m, and on the corresponding switching of the controlled system from one to another of m+1 different structures. Yet, some problems arise when uncertainties are present in some matrices characterizing the controlled systems. In this paper, conditions are identified under which, even in the uncertain case, 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