Slide mode control design for a class of uncertain dynamic systems

In this paper, the problem of designing a sliding mode control law for uncertain systems where the uncertainty in the state model does not satisfy the matching condition is considered. Based on the linear matrix inequality approach, a sufficient condition is proposed for the existence of linear sliding surfaces guaranteeing that the system in sliding mode is asymptotically stable. Sliding mode control laws are designed such that the system states reach the sliding surface and stay on it thereafter. Finally, the advantages and effectiveness of the proposed approaches are demonstrated via a numerical example.