This paper considers the problem of robustly stabilizing an uncertain system via fixed-order output feedback control. This problem is considered by defining a notion of robust stabilizability with a quadratic storage function. This notion is closely related to the notion of quadratic stabilizability. The main result of the paper shows that if an uncertain system is robustly stabilizable with a quadratic storage function via a nonlinear time-varying controller, then it will also be robustly stabilizable with a quadratic storage function via a linear time-invariant controller of the same order.