Abstract: The method for the linear system with time－varying norm－bounded uncertainties was presented to reject periodic disturbances and to track periodic reference signals with a known period effectively，which can design the low－pass filter in the repetitive controller and the output feedback controller simultaneously．The repetitive control system was converted to a time－delay system；Based on Lyapunov theory，a sufficient condition was derived in terms of a linear matrix inequality （LMI），which ensures robust stability of the time － delay system．Based on the derived condition，the problem of designing the low－pass filter and the output feedback controller was converted to a nonlinear matrix inequality problem．By using the linear matrix inequality （LMI） and cone complementarity linearization （CCL） algorithm，an iterative algorithm was presented to calculate the larger cut－off angular frequency of a low－pass filter and the corresponding output feedback controller parameters．The numerical example is presented to illustrate the validity of the proposed method．

Key words: Repetitive control system , Linear matrix inequality , Cone complementarity linearization algorithm , Output feedback controller , Tracking accuracy

摘要： 针对具有时变范数有界不确定性的线性系统，为了有效地抑制周期性扰动和跟踪周期性参考输入信号，提出一种同时设计重复控制器中的低通滤波器和输出反馈控制器的方法。首先，将重复控制系统转化为时滞系统；采用 lyapunov稳定性理论得到该时滞系统的鲁棒稳定性条件。基于此条件，将设计低通滤波器和输出反馈控制器的问题转换成一个非线性矩阵不等式求解问题，利用线性矩阵不等式方法(LMI)、锥补线性化方法(CCL),通过所提出的迭代算法计算低通滤波器最大的剪切频率及其对应的输出反馈控制器参数。仿真示例验证了所提出方法的有效性。

关键词: 重复控制系统 , 线性矩阵不等式 , 锥补线性化 , 输出反馈控制器 , 跟踪精度