An LMI-based switching surface design method for a class of mismatched uncertain systems

In this note, we consider the problem of designing linear sliding surfaces for multivariable uncertain systems with mismatched uncertainties in the state matrix. In terms of linear matrix inequalities, we give a new invariance condition guaranteeing the existence of a linear switching surface such that the reduced-order equivalent sliding mode dynamics restricted to the switching surface is not only stable but completely invariant to mismatched uncertainties. We also give an explicit formula of such linear switching surfaces, together with a design example.