The contribution of this paper is a new, observer-free output feedback cooperative control architecture for continuous-time, minimum phase, and high-order multivehicle systems in the context of a containment problem (i.e., outputs of the follower vehicles convergence to the convex hull spanned by those of the leader vehicles). The proposed architecture is predicated on a nonminimal state-space realization that generates an expanded set of states only using the filtered input and filtered output and their derivatives for each follower vehicle, without the need for designing an observer for each vehicle. Specifically, the proposed observer-free output feedback control law consists of a vehicle-level controller and a local cooperative controller for each vehicle, where the former addresses internal stability of vehicles and the latter addresses the containment problem. Two illustrative numerical examples complement the proposed theoretical contribution.