Design of fractional order sliding mode controller via non-integer order backstepping by fractional order derivative of Lyapnov function

Novel sliding mode control design is proposed for a fractional order system in the presence of disturbance and nonlinear terms on mismatched input channel. This mismatched-channel situation is overcome by using the backstepping method. To authors best knowledge, this is first time to present the noninteger order backstepping approach. In order to demonstrate our design efficiency, some numerical simulations are shown.