Abstract: A convergence condition of Proportion, Integral and Derivative（PID） iterative learning fault-tolerant controller is proposed for linear time-varying system with actuator fault. An open-loop PID iterative　learning fault-tolerant controller is designed for time-varying repeat system, and a sufficient condition for the existence of the PID controller is analyzed based on [λ]-norm. The convergence condition of PID fault-tolerant controller is changed as Linear Matrix Inequality（LMI） based on Schur complement principle, under the presetting iterative learning convergence rate, the optimal control gains can be determined by using LMI, it avoids the blindness of the iterative control gain settings. The numerical simulation of rotational control system verifies the ability of fault tolerance and tracking performance of PID iterative fault-tolerant controller.

Key words: continuous time-varying system, actuator fault, iterative learning, Proportion, Integral and Derivative（PID） control, linear matrix inequality

摘要： 对存在执行器故障的连续线性时变系统，给出了PID型迭代学习容错控制律的收敛条件。对连续时变故障系统设计了一种PID迭代学习容错控制律，在[λ]范数意义下给出了故障系统PID型迭代容错控制器收敛的充要条件；基于Schur补原理和不等式变换，将容错控制器收敛条件转换成线性矩阵不等式，当迭代学习收敛速度设定时，基于线性矩阵不等式能快速确定最优迭代控制增益，避免了迭代控制增益设置的盲目性。旋转控制系统的数值仿真，验证了PID迭代容错控制器优良的容错性能和跟踪性能。

关键词: 连续时变系统, 执行器故障, 迭代学习, PID控制, 线性矩阵不等式