针对一类含有非周期性扰动的不确定线性系统，提出一种基于滑模变结构重复控制系统设计方法。首先，建立基于改进型重复控制器、反馈控制器和被控对象的增广系统结构模型，获得其状态空间模型。然后，在此基础上，针对增广控制对象，在保证系统稳定的前提下，设计滑模控制器，利用Lyapunov稳定性原理推导出滑模变结构重复控制系统稳定的线性矩阵不等式条件；最后，通过仿真实验验证方法的有效性。

This paper concerns the problem of designing a robust sliding-mode based modified repetitive-control system (MRCS) for a class of uncertain plants with aperiodic disturbances. An augmented system is first constructed, which contains a repetitive controller, a sliding mode controller and a feedback controller. And its state-space model is presented. Next, the stability condition for the MRCS is established which can be directly used to design the parameters of the repetitive controller and the feedback controller. Then, for the augmented system, the Lyapunov stability theory is used to derive a linear-matrix-inequality (LMI) based robust stability condition. Based on the stability condition, a design algorithm for the gains of the sliding-mode controller is constructed. Finally, a numerical example demonstrates the validity of the method.