Abstract:The optimal sliding surface and variable structure control are developed for discrete time-delay systems. In the optimal sliding surface designing process, by using the successive approximation approach (SAA), the two-point boundary value (TPBV) problem with time-delay and time-advance terms is transformed into a sequence of TPBV problems without time-delay and time-advance terms. The sequence of the solutions uniformly is proved converge to the optimal sliding surface and the controller is designed.