Delay-independent variable structure control of time-delay systems with mismatched uncertainties

A variable structure control method is proposed for a class of time-delay systems with mismatched norm-bounded uncertainties. We relax the matching assumption of traditional VSC design method, and the uncertain system under consideration may have mismatched parameter uncertainties in the state matrices as well as in the input matrix. In terms of linear matrix inequalities (LMIs), we give a delay-independent sufficient condition for the existence of sliding mode surface, on which sliding mode dynamics is asymptotically stable. A variable structure control law is also designed to guarantee system trajectories reach the sliding mode surface. Finally we give an example to show the effectiveness of our method.