The problem of designing an output feedback control law which exponentially achieves output regulation is considered for known stabilizable and detectable linear systems which are allowed to be non-minimum phase; output references and/or additive disturbances are both generated by a linear exosystem with unknown purely imaginary eigenvalues and uncertain order. The novelty of this note is to require only an upper bound on the exosystem order to achieve a global solution which includes exponentially convergent estimates of the exosystem unknown frequencies.