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.

在离散滑模控制器理论中，对不确定性和扰动的敏感性问题仍然是一个具有挑战性的任务。在本文中，提出了仅使用具有周期性扰动的线性时变系统的输入-输出测量的离散重复自适应滑模控制。考虑干扰周期性的新的间接自适应算法用于识别所考虑系统的参数变化。基于此识别，开发了离散滑模控制器。然后，将插入式重复控制的结构集成到先前的控制器中，以消除谐波干扰。进行了鲁棒性分析，以确保所提出控制器的渐近稳定性。