ISS properties of sliding-mode controllers for systems with matched and unmatched disturbances

In this paper we present a controller that achieves global input-to-state stability for a linear system of arbitrary relative degree, subjected to matched and unmatched disturbances. This controller combines the properties of a discontinuous term, and a linear one, enforcing a conventional sliding mode using only partial state information. A direct and simple way of choosing the gains for this controller is also provided.