This article contributes to a detailed convergence analysis of iterative learning control for singular conformable differential equations with one-sided Lipschitz nonlinearity. In order to track the desired reference trajectory in a finite time interval, a closed-loop D-type learning update law is proposed for such nonlinear systems. Here, the strict convergence analysis is derived under the condition of identical initial state. A numerical example is provided to verify the effectiveness of the proposed controller. K E Y W O R D S convergence, iterative learning control, singular conformable differential equations 1 INTRODUCTION Iterative learning control is an accurate technology, which is suitable for the systems with repetitive motion in a finite time interval. Its goal is to achieve perfect tracking task. The concept of iterative learning control was first mentioned by Uchiyama, a Japanese scholar, in a paper on robot control. 1 A few years later, Arimoto and others formally proposed iterative learning control based on Reference 2. The principle of iterative learning control is: through the control attempt of the controlled system, the deviation between the output signal and the desired target is corrected to improve the tracking performance of the system. At the same time, it attracts a large number of researchers and has achieved a large number of scientific research results. 3-10 Singular system is a kind of system described by differential and algebraic equations. Compared with the regular system described only by differential or difference equations, it has algebraic equation description part. Because of different research fields, singular systems are called by different scholars in different fields, such as generalized state space system, descriptor system, and so on. The singular system includes the description of algebraic equation. Therefore, the applicability of singular system is much wider than that of normal system. The original singular system model was proposed by Ardema in 1962 when studied the dynamic model of spacecraft. Since then, the majority of research enthusiasts have carried out extensive research on singular systems, and obtained many very valuable theoretical results. In the field of Physics, Solimene et al 11 dealt with the calculation of the singular system of radiation operators related to the banded current case. And it can be easily used to describe biological systems in practice. 12,13 Ma and Boukas, 14 based on a singular