This article considers the robust containment control problem of heterogeneous linear multi-agent systems subject to structured uncertainties and external disturbances. By introducing a new neighborhood error of follower agents, the containment control problem can be formulated into output regulation problem.By employing a distributed compensator and robust H ∞ control approach, sufficient conditions in terms of linear matrix inequalities are derived to ensure that all followers asymptotically converge to the convex hull spanned by the leaders with the prescribed H ∞ performance under fixed topology. A numerical example is provided to verify the effectiveness of the proposed method.