Abstract: To solve the convergence speed problem in the design process for iterative learning algorithms for singular systems, we propose a class of second-order iterative learning algorithms based on the singular value decomposition method for singular systems. In addition, we discuss the convergence rate for iterative learning control algorithms for singular systems with the help of the Q factor method. This method can transform the convergence speed of the algorithm into a Q factor size problem. The numerical simulation shows that the iterative learning control system converges to the desired trajectory after the finite operation, and the convergence speed of the algorithm is related to the value of the algorithm gain matrix.