This technical note studies the cooperative global robust output regulation problem for a class of nonlinear multi-agent systems with switching network by a distributed output feedback control law. We first convert the problem via the internal model approach to a global robust stabilization problem of an augmented system. Then, using average dwell time method, we present a set of solvability conditions for the latter problem by a distributed switched output feedback control law, thus leading to the solution of the original problem. Our approach is illustrated by a family of Lorenz systems subject to a harmonic exosystem.