Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems

This article investigates a novel sliding model control approach for a class of nonlinear fractional order systems. In particular, the sliding surface with additional nonlinear part is designed by a Lyapunov-like function and one can achieve much more satisfying system performances by selecting suitable parameters. Moreover, a second-order switching law is generated from the commonly used adaptive switching law. Its properties are carefully discussed, and it is proven that the reaching time of the sliding surface can be guaranteed nonsensitive to the initial conditions with the second-order switching law, while the adaptive switching law cannot even guarantee the finite-time convergence. Then the stability of the closed-loop control system is rigorously analyzed via indirect Lyapunov method. Finally, simulation examples are presented to illustrate the effectiveness of the proposed control method.