The structure of linear, time-invariant, completely controllable and observable multivariable systems under the action of constant output feedback control laws is studied. A structure theorem is stated and proved. Following Dickinson (1976), the notion of covariant output feedback control laws is introduced. It is shown that these results can be used to investigate the problems concerning (i) our ability to alter some of the Popov (1972) invariants by employing constant output feedback control, and (ii) the asymptotic behaviour of the closed loop poles under the variation of the output feedback gain matrix.