In this paper, we investigate the problem of semiglobal minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that in the absence of minimal time singular trajectories, the solutions of the closed-loop system converge to the origin in quasi-minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances, and actuator noise.