In this paper, we consider the robust non-fragile $H_{infty}$ output feedback controller design method for uncertain descriptor systems with feedback and observer gain variations. The existence condition of observer-based robust and non-fragile $H_{infty}$ output feedback controller and the controller design method are Presented on the basis of linear matrix inequality approach. The proposed robust non-fragile $H_{infty}$ output feedback controller guarantees asymptotic stability, non-fragility, $H_{infty}$ norm bound within a prescribed level in spite of disturbance, parameter uncertainty, and feedback/observer gain variations.