New Discrete Sliding Mode Control for Nonlinear Multivariable Systems: Multi-Periodic Disturbances Rejection and Stability Analysis

The Sliding Mode Control (SMC) is well known by its robustness to parameter uncertainties or external disturbances. The repetitive control (RC) is able to track or reject periodic and multi-periodic signals. This paper presents a new control strategy as a combination of a Sliding Mode approach and Repetitive Control to reject periodic and multi-periodic disturbances in the case of nonlinear multi-input discrete-time systems. A stability analysis of the new repetitive discrete sliding mode control is then proposed. The simulation results show the effectiveness of the proposed control to reject periodic and multi-periodic disturbances.