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In this work, a discrete second order sliding mode control with a new sliding function for a linear uncertain system with state delay is proposed. The systems are assumed to have structured mismatched time varying uncertainties. Firstly, a new sliding function include a present and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities (LMI). Then, a robust discrete second order sliding mode controller with this new function is investigated to overcome the effect of time delay and uncertainties in the closed loop. A numerical example illustrates the effectiveness and the advantages of the proposed approach.

The problem of sensitivity to uncertainties and disturbances is still a challenging task in the theory of discrete sliding mode controller. In this article, a discrete repetitive adaptive sliding mode control using only input-output measurements of linear time-varying system with periodic disturbances is proposed. A new indirect adaptive algorithm taken into account the periodicity of disturbances is used to identify parameter variations of the considered system. Based on this identification, discrete sliding mode controller is developed. Then, the structure of plug-in repetitive control is integrated into the previous controller to reject harmonic disturbances. A robustness analysis is achieved to ensure the asymptotic stability of the proposed controller. An example of time-varying DC-DC buck converter subject to harmonic disturbances is carried out to illustrate the effectiveness of the designed discrete repetitive adaptive sliding mode control.

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