Sliding mode control of generalized fractional chaotic systems

A sliding mode control technique is introduced for generalized fractional chaotic systems. These systems are governed by a set of fractional differential equations of incommensurate orders. The proposed design method relies on the fact that the stability region of a fractional system contains the stability region of its underlying integer-order model. A sliding mode controller designed for an equivalent integer-order chaotic system is used to stabilize all its corresponding fractional chaotic systems. The design technique is demonstrated using two generalized fractional chaotic models; a chaotic oscillator and the Chen system. The effect of the total fractional order is investigated with respect to the controller effort and the convergence rate of the system response to the origin. Numerical simulations validate the main results of this work.