Iterative Learning Control for 2-D Discrete Systems in Frequency Domain

In this paper, the robust convergence problem of iterative learning control (ILC) is investigated for two-dimensional (2-D) discrete systems with iteration-varying boundary states and errors in the frequency domain. A classical P-type ILC law is designed. By using 2-D Z-transform analysis, a sufficient condition of the ILC law can be obtained. By the rigorous mathematical proof, the ultimate ILC tracking error can converge to a bounded region, which is dependent on the upper bound of boundary states/errors. In particular, when all the boundary states and errors are zero, the practical tracking output can precisely track a 2-D desired trajectory.