Variable structure control of dynamical systems with mismatched norm-bounded uncertainties: An LMI approach

In this paper, we propose a new sliding surface design method for a class of uncertain systems with mismatched unstructured uncertainties. We relax the matching assumption of traditional VSC design methods, and the uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as the input matrix. In terms of linear matrix inequalities (LMIs), we give a sufficient condition for the existence of linear sliding surfaces guaranteeing asymptotic stability of the reduced-order equivalent sliding mode dynamics. We give an LMI parameterization of such sliding surfaces together with a switched feedback control strategy. We also give an LMI existence condition of linear sliding surfaces guaranteeing the prescribed decay rate. Finally, we give simulation results to show the effectiveness of our method.