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Discrete simplex sliding mode control and its application to singular perturbation systems

The design of a simplex sliding mode control scheme for a linear discrete system is developed in this paper. In order to reduce the inherent disadvantage of the chattering problem, a modified simplex method is also proposed to improve response performance. The authors utilize this method to design a sliding mode controller for singularly perturbed discrete systems. 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 scheme.