A systematic optimisation approach to robust eigenstructure assignment for control systems with output feedback is presented. The proposed scheme assigns the maximum allowable number of closed-loop eigenvalues to desired locations, and determines the corresponding closed-loop eigenvectors as close to desired ones as possible. Additionally, the stability of the remaining closed-loop eigenvalues is guaranteed by the satisfaction of an appropriate Lyapunov equation. The overall design is robust with respect to time-varying parameter perturbations. The approach applied to a literature example, where it is shown to capture the shape of the desired transient response.