This paper addresses convergence of iterative learning control for impulsive linear discrete delay systems with randomly varying trial lengths when coefficient matrices of systems are permutable. With the aid of the explicit representation of solutions expressed in discrete matrix delayed exponential, we provide two sufficient conditions of convergence to guarantee that tracking errors uniformly converge to zero in the sense of expectation for the above impulsive controlled systems by designing two proper update learning laws with the modified tracking errors. Finally, two illustrative examples are given to verify the theoretical results.

中文翻译：

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脉冲线性离散延迟系统迭代学习控制的收敛性分析

本文讨论了当系统的系数矩阵可置换时，具有随机变化试验长度的脉冲线性离散延迟系统的迭代学习控制的收敛性。借助离散矩阵延迟指数表示的解的显式表示，我们提供了两个充分的收敛条件，通过设计两个适当的更新学习律来保证跟踪误差在上述脉冲控制系统的期望意义上一致收敛到零与修改后的跟踪误差。最后，给出了两个说明性例子来验证理论结果。