Second order sliding mode control for nonlinear affine systems with quantized uncertainty

This paper deals with the design of a Second-Order Sliding Mode (SOSM) control algorithm able to enhance the closed-loop performance depending on the current working conditions. The novelty of the proposed approach is the design of a non smooth switching line, based on the quantization of the uncertainties affecting the system. The quantized uncertainty levels allow one to define nested box sets in the auxiliary state space, i.e., the space of the sliding variable and its first time derivative, and select suitable control amplitudes for each set, in order to guarantee the convergence of the sliding variable to the sliding manifold in a finite time. The proposed algorithm is theoretically analyzed, proving the existence of an upper bound of the reaching time to the origin through the considered quantization levels.