Abstract: We propose finite-frequency iterative learning control algorithm based on output information herein for a class of state-unmeasurable spatially interconnected systems with periodic interconnection characteristics. We transform the two-dimensional spatially interconnected systems into one-dimensional equivalent model by lifting the variable of the discrete space model coupled with multiple subsystems. Then, we use the output information to construct an iterative learning control law, which converts the controlled system into an equivalent repetitive process model. Subsequently, on the basis of the generalized KYP lemma, the performance index conditions that guarantee the stability of discrete repetitive process along the trail and the monotone asymptotic convergence of tracking errors in different frequency intervals are transformed into linear matrix inequality. Finally, the effectiveness of the proposed algorithm is demonstrated through the control simulation of the active ladder circuts.