Adaptive sliding mode control for uncertain general fractional chaotic systems based on general Lyapunov stability

This work focuses on general Lyapunov stability of general fractional differential systems (GFDSs), as well as adaptive sliding mode control (ASMC) of uncertain general fractional chaotic systems (UGFCSs) with uncertainty and external disturbance. Initially, the existence and uniqueness theorem and general Lyapunov stability criterion for GFDSs are presented and verified. Furthermore, general fractional sliding surface (GFSS) is developed. With the proposed stability criterion, it is shown that the states of UGFCSs can reach GFSS in a finite–time interval and asymptotically converge to zero along GFSS. Lastly, the efficacy and efficiency of the proposed fractional controller are demonstrated by numerical simulations.