Sliding mode control based on finite time stabilization

In order to make that the perturbation is minimal, the perturbation is provided into two parts by projection matrix — the matched and unmatched perturbation. The controller design uses integral sliding mode concept and contains two parts. A part achieves finite time stabilization of the dynamics with unmatched perturbation combined with H ∞ method. The other part rejects bounded matched perturbation throughout the entire response of the system. The time convergence is chosen in advance.