Variable structure control design for time-delay systems

We propose a variable structure control design method for a class of multivariable uncertain state-delayed systems which can be represented by polytopic models. In terms of LMIs, we derive a sufficient condition for the existence of a linear sliding surface guaranteeing the asymptotic stability of the sliding mode dynamics. We parameterize the sliding surface by using the solution of the LMI existence condition. We also give a switching feedback control strategy guaranteeing stable sliding mode. By using a numerical example, we show that our method supplements the existing results and it can be better than the existing results.