Variable structure control of discrete uncertain system with time-delays

The original discrete uncertain system with time-delay is simplified to a discrete uncertain system without time-delay and a switching function is designed in which the movement of system is asymptotically stable. Then a variable structure controller is designed, which can force the system trajectory arrive at the quasi-switching manifold in limited steps and can traverse the switching manifold each step and can decreasingly approach to zero. Finally, Effectiveness of the proposed control method is demonstrated by simulation example.