Integral sliding mode control for linear time-invariant implicit descriptions

We propose an integral sliding surface for linear time-invariant implicit descriptions (descriptor systems). We show that, under reasonable assumptions (regularity, stabilizability and a corresponding matching condition), it is possible to design a controller that drives the descriptor variables to zero, even in the presence of disturbances. Higher-order sliding motions are required since, for the solutions of the implicit description to be well defined, special care must be taken on the degree of smoothness of the controller and the perturbations.