Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics

Sliding mode control approaches are developed to stabilize a class of linear uncertain fractional-order dynamics. After making a suitable transformation that simplifies the sliding manifold design, two sliding mode control schemes are presented. The first one is based on the conventional discontinuous first-order sliding mode control technique. The second scheme is based on the chattering-free second-order sliding mode approach that leads to the same robust performance but using a continuous control action. Simple controller tuning formulas are constructively developed along the paper by Lyapunov analysis. The simulation results confirm the expected performance.