Output feedback sliding mode control of systems with bounded disturbances

This paper considers linear systems with bounded disturbances, that are not necessarily matched. A static output feedback sliding mode controller is designed. The existence problem is solved by determining a sliding surface that minimizes the ultimate bound of the reduced-order dynamics in the presence of unmatched disturbances. Linear Matrix Inequalities (LMIs) are derived to compute the sliding surface via a descriptor approach. Then, a gain of the switching function that guarantees that the sliding mode is reached is found using LMIs. In the case of matched disturbances, the controller provides exponential stability, whereas in the case of unmatched disturbances the ultimate bound is defined by the reduced-order dynamics and is proportional to the bound on the matched disturbances. A numerical example from the literature illustrates the proposed method.