We report observations of stabilized traveling-wave (TW) convection in a regime in which the uncontrolled system exhibits repeated, erratic growth and abrupt decay of spatially localized bursts of TW. By applying as feedback a spatially varying Rayleigh-number profile computed from the measured convection pattern, we suppress this behavior and stabilize states of unidirectional TW with spatially uniform amplitude on the unstable branch of the subcritical bifurcation to convection. This allows us to measure the nonlinear coefficients of the corresponding quintic complex Ginzburg-Landau equation.