This paper addresses the cooperative search of static ground targets by a group of Unmanned Aerial Vehicles (UAVs) over some region of interest. The search strategy dependents on the availability and accuracy of the information collected. When a target is detected, a probabilistic description of the measurement noise is usually considered, as well as probabilities of false alarm and non-detection, which may prove difficult to characterize a priori. An alternative modeling is introduced here. The ability to detect and identify a target depends deterministically on the point of view from which the target is observed. Introducing the notion of detectability sets for targets, we propose a robust distributed set-membership estimator to provide set estimates of target locations. The obtained set estimates are guaranteed to contain all target locations when the search is completed. The target search is formulated as a multi-agent cooperative control problem where the control inputs are obtained using a Model Predictive Control (MPC) approach minimizing a measure of the set estimates representing the detection performance. The proposed set estimator and cooperative control scheme are distributed, i.e., accounting only for information from neighbors within communication range. The effectiveness of the proposed algorithm is illustrated by simulation.