This paper first investigates convergent property of two iterative learning control (ILC) laws for two kinds of two-dimensional linear discrete systems described by the first Fornasini–Marchesini model (2-D LDFFM with a direct transmission from inputs to outputs and 2-D LDFFM with input delay). Different from existing ILC results for 2-D LDFFM, this paper provides convergence analysis in a three-dimensional (3-D) framework. By using row scanning approach (RSA) or column scanning approach (CSA), it is theoretically proved no matter which method is adopted, perfect tracking on the desired reference surface is accomplished. In addition, linear matrix inequality (LMI) technique is utilized to computer the learning gain of the ILC controller. The effectiveness and feasibility of the designed ILC law are illustrated through numerical simulation on a practical thermal process.

中文翻译：

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两类二维线性离散Fornasini-Marchesini模型的迭代学习控制的收敛性分析

本文首先研究了两种迭代学习控制（ILC）律对两种二维线性离散系统的收敛性，这两个线性离散系统由第一个Fornasini-Marchesini模型（2-D LDFFM，具有从输入到输出的直接传输和2-D具有输入延迟的LDFFM）。与现有的针对2-D LDFFM的ILC结果不同，本文提供了在三维（3-D）框架中的收敛分析。通过使用行扫描方法（RSA）或列扫描方法（CSA），理论上证明无论采用哪种方法，都可以在所需的参考面上实现完美的跟踪。另外，线性矩阵不等式（LMI）技术用于计算机化ILC控制器的学习增益。