Comparison between two different sliding mode controllers for a fractional-order unified chaotic system

Two different sliding mode controllers for a fractional order unified chaotic system are presented. The controller for an integer-order unified chaotic system is substituted directly into the fractional-order counterpart system, and the fractional-order system can be made asymptotically stable by this controller. By proving the existence of a sliding manifold containing fractional integral, the controller for a fractional-order system is obtained, which can stabilize it. A comparison between these different methods shows that the performance of a sliding mode controller with a fractional integral is more robust than the other for controlling a fractional order unified chaotic system. (general)