In an ideal environment, an exact model matching (EMM) system is internally stable and the plant output follows perfectly the reference model output. In a real environment, however, there are many kinds of harmful perturbation, which cause not only tracking error but even instability for some kinds of perturbation. There are two free polynomials q(s) and gamma(s), the former being the characteristic polynomial of the reduced order state observer, and the latter being an interactor of scalar version. The function of controller depends on the choice of these polynomials. Robust EMM design is defined as the proper choice of these polynomials so as to strengthen the robustness against perturbation as much as possible. II is shown that the controller function does not depend on these polynomials independently but on the product q(s)gamma(s). Robust EMM design is examined for each perturbation of nonzero initial conditions, input disturbance, unmodeled dynamics and incorrect implementation of controller.