Stability analysis of quantized iterative learning control systems using lifting representation

Summary This paper presents a stability analysis of the iterative learning control for discrete‐time systems with data quantization. Three quantized iterative learning control schemes are considered by using different quantized signals, including system output quantized signal, tracking error quantized signal, and control input quantized signal. The logarithmic quantizer is introduced to decode these signals with a number of quantization levels, and the sector bound method is used to deal with the quantization error. Based on the supervector formulation for iterative learning control systems, some convergence conditions for these iterative learning control laws are given, respectively. It is shown that iterative learning control laws with system output quantized signal and control input quantized signal only guarantee that the tracking error converges to a bound and the bound depending on quantization density and desired trajectory. Thus, the iterative learning control law with tracking error quantized signal can obtain zero tracking error. These results are illustrated by 2 examples.