Control Of A Class Of Caputo Fractional-order Chaotic Systems Via Sliding Mode

This paper mainly studies the asymptotic stability problem of a class of three-dimensional Caputo fractional order chaotic systems. First, by using the sliding mode control, we designed the control law to control different variables and obtained the asymptotic stability condition of the fractional order chaotic system which is proved by the Lyapunov stability theorem. Then when the fractional order chaotic system is subject to external disturbance and parameter perturbation, we exploited the same control law to control the system due to the fact that the design of the sliding mode control are independent of the external disturbance and parameter perturbation, and obtained the sufficient conditions to make the fractional order chaotic system asymptotically stable. Finally, several examples are given to illustrate the conditions of asymptotic stability of the fractional order chaotic system.