Synchronization of fractional-order chaotic systems based on the fractional-order sliding mode controller

For synchronization of fractional-order chaotic systems, this paper presents a novel fractional-order sliding mode controller, in which fractional calculus is introduced to the sliding mode control. Based on Lyapunov stability theory and fractional-order system's stability theorem, stability analysis is performed. Two examples are given respectively, which include synchronization of two identical fractional-order systems (Chen-Chen) and synchronization of two non-identical fractional-order systems (Chen-Liu). Numerical simulations illustrate the effectiveness of the proposed controller.