A PI design method for faulty networks is provided based on Linear Matrix Inequalities (LMIs). Feedback controllers for irrigation canals are designed based on LMIs, but sparsity constraints are also imposed to make zero the feedback control law elements not corresponding to the tuning PI parameters. Therefore, the design method is halfway between a PI controller and an optimal feedback control law, also providing stability guarantees up to a maximum probability of packet losses. The objective of the downstream controller is to maintain the water levels upstream from each downstream check structure of each canal pool, while gravity-offtake gates satisfy downstream water demands. The proposed approach is tested using the irrigation system of ASCE Test Canal 1 and compared with other tuning methods via simulation. Our results show that the design method can be a useful tool when dealing with control systems under faulty networks.