Discrete input-output second order sliding mode control using LMIs approach

During the reachability phase, the sliding mode control is sensitive to external disturbances and uncertainties. In this paper, we propose to determine the coefficients of the sliding function using the technique of Linear Matrix Inequalities. This technique leads to an optimal choice of sliding function. Using the proposed sliding function, a discrete second order sliding mode control is presented. The control law is based on an input-output model. Simulation results demonstrate that the proposed strategy leads to an optimal performances in terms of the reduction of the reachability phase and the chattering phenomenon.