AbstractIn this paper, open loop and closed loop PDα‐type fractional‐order iterative learning control algorithms with fixed topology for the fractional‐order distributed multi‐agent systems are proposed. In the sense of Lebesgue‐p norm, the convergences of the proposed methods are discussed by using the generalized Young inequality of convolution, and their convergence conditions are presented. The proposed algorithm extends the application scope of traditional iterative learning control theory. Theoretical analysis shows that by selecting the appropriate learning gain matrix, the output of each agent can completely track the desired trajectory in a limited time interval as the number of iterations increases. The feasibility and theoretical correctness of the presented algorithm are verified by numerical simulations.