Sliding mode control of a class of fractional chaotic systems in the presence of parameter perturbations

This paper deals with a sliding mode control for a class of fractional uncertain chaotic systems under perturbations of parameters. A fractional integral sliding surface is proposed for fractional-order systems and then the sliding mode control technique is carried out to realize the control of the given systems. Based on Lyapunov stability theory, we theoretically verify that the controller is effective, and the designed control scheme can go against the system's uncertainty to guarantee the property of asymptotical stability in the presence of parameter fluctuations. Later, two typical examples are illustrated numerically to show that the control approach in this paper is capable for any form of fractional-order uncertain systems.