Constrained sliding mode control of nonlinear fractional order input affine systems

Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt. The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time. To eliminate the chattering in the sliding mode and make the input controller bounded, hyperbolic tangent is used for designing the proposed fractional order sliding surface. Finally, the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory. A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case. Finally, simulation results are provided to show the effectiveness of the designed controller.