A Backstepping Design with Sliding Mode Control for Uncertain Discrete System

The technique of backstepping have can avoid cancellations of useful nonlinearities. It is widely used in nonlinear adaptive control. But it is difficult to use this technique for uncertain nonlinear systems. Sliding mode control has robustness and application with feedback linearization. This paper shows that the robustness can be used for back stopping technique to solve the uncertainty problem and to improve the scalar design problem using Control Lyapunov function which is the motivation of back stepping technique with recursive design for high-order systems. In the respect of SMC, the result of this paper does not need to satisfy the matching condition.