Adaptive robust sliding mode control for time-varying delay systems with uncertainties

This paper study the adaptive robust sliding mode controller design of a class of uncertain systems with time-varying delay. The uncertainty is norm-bounded, but the upper bound is unknown. Firstly, an integral sliding surface is designed so that the reaching phase has been eliminated. A sufficient condition such that the sliding mode is asymptotically stable is given in term of LMIs(Linear Matrix Inequality). The condition involves a few matrix variables but could reduce the conservatism. A new adaptive law is presented to estimate the unknown upper-bound of the uncertainty. Then a sliding mode based controller is proposed so that the system state stay on surface. Finally, an example is given to show the effectiveness of this method.