Ship deck landing control of a quadrotor requires certain robustness with respect to ship heave motion. Typical systems only provide relative height, therefore do not have relative heave rate information. In this paper, a linear output feedback control consisting of a full state feedback controller and a Luenberger observer is formulated. Invariant ellipsoid method is used to formulate an estimation of a bound on the response of a linear output feedback-controlled system subjected to external disturbances and measurement noise. The gains that result in a minimum bound are optimized using a gradient descent iterative approach proposed in this paper where the invariant ellipsoid condition is linearized into a tractable LMI condition. This approach is applied to a simulation of a quadrotor landing on a ship deck and results are compared with other gains. The gains selected using the proposed approach exhibits improved robustness to external disturbances and measurement noise.