Design of variable structure control for mismatched uncertain singular systems

The design problem of variable structure control for a class of linear singular System with unmatched uncertainties in the state matrix was studied. The equivalent restrict decomposition form was eatablished for the singular System with mismatched uncertainties. On the basis of this form, the switching surface was designed using the linear matrix inequality (LMI) method, and a variable structure control law, which ensures the System state to reach the switching surface, was presented. A simulation example shows that the design method guaranteed not only the sliding mode of the system state trajectory to be realized, but also the sliding mode to be regular, impulse-free, and asymptotically stable.