On the sliding-mode control of fractional-order nonlinear uncertain dynamics

This paper deals with applications of sliding-mode-based fractional control techniques to address tracking and stabilization control tasks for some classes of nonlinear uncertain fractional-order systems. Both singleinput and multi-input systems are considered. A second-order sliding-mode approach is taken, in suitable combination with PI-based design, in the single-input case, while the unit-vector approach is the main tool of reference in the multi-input case. Sliding manifolds containing fractional derivatives of the state variables are used in the present work. Constructive tuning conditions for the control parameters are derived by Lyapunov analysis, and the convergence properties of the proposed schemes are supported by simulation results.