Abstarct: Backstepping method is a strong method of robust control field. In this thesis, this method is used to control nonlinear cart and pole system. Since the equations of this system is not in a form that can design conventional backstepping controller for it, a new method called is used to stabilization of it. In this method no need to transform system equations. Also external disturbance applied to the system with its specific upper bound condition, is considered as the uncertainty. Therefore the controller is robust against uncertainty. Modeling of physical systems is always associated with uncertainty. Since the design of controller with this approach requires precise dynamic model of the system, in the next step the fuzzy inference system with adaptive mechanisms is used to approximate the dynamics of the system. In each two step, simulations results is compared with decoupled sliding mode control. In this thesis, the stability of the system is proved using Lyapunov method.