Design of sliding mode controllers for nonlinear fractional-order systems via diffusive representation

In this paper, the design of first- and second-order sliding mode controllers for fractional-order nonlinear systems is addressed. The key concept used here is the diffusive representation of the fractional-order nonlinear systems. We show that the use of diffusive representation is an interesting alternative way to overcome some hard mathematical manipulations encountered with fractional-order operators. Sufficient reaching conditions to the sliding manifold are established for both first- and second-order sliding mode controllers. Numerical application to chaos control is given to illustrate the efficiency of the proposed approach.