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

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