Backstepping tracking control for a class of discrete-time nonlinear systems in pure-feedback form

In this paper, a new control scheme is proposed for a class of pure-feedback nonlinear discrete-time systems by using backstepping technique. This problem is considered difficult to be dealt, mainly because that the triangular structure of pure-feedback systems has no affine appearance of the variables to be used as virtual controls. After the pure-feedback form is transformed into a cascade form, the feedback tracking controller is developed by using backstepping procedure. Under appropriate assumptions, the closed-loop nonlinear discrete-time system is uniformly ultimately bounded. The stability of the close-loop system is proved based on Lyapunov theorem. Simulation studies are conducted to illustrate the effectiveness of the proposed approach.