A sliding hyperplane design method for a class of linear systems with unmatched disturbances

The paper studies sliding mode (SM) features in systems characterized by the presence of unmatched disturbances. Although it is possible to establish a SM in such systems, the unmatched part of disturbances has impact on the SM dynamics. Under these circumstances system trajectory does not converge to the origin but wanders in its neighborhood along the sliding manifold. This paper offers a sliding hyperplane design method to minimize the effects of the unmatched disturbances upon the SM dynamics, for a class of linear systems. The optimization criterion is minimization of the steady state vector norm. The suggested approach has been demonstrated on a numerical example.