Simplex sliding mode control of singular perturbation systems

The design of the sliding mode control with simplex method for the singular perturbation system is investigated in this paper. The simplex method, to the design of the sliding mode, is easy and brief. This method, however, has an inherent disadvantage that the chattering problem always exists. This paper makes a few modification for simplex method to reduce chattering and improve performance. We will utilize this method to design the sliding mode controller for the singular perturbation system. The exact upper bound of the parasitic parameter is also determined. Finally, an example is illustrated to verify the effectiveness of the simplex method in the design of the sliding mode control.