We investigate the existence and uniqueness of robust time-optimal control solutions of flexible structures for rest-to-rest motion. We show that several robust time-optimal control designs for flexible systems are equivalent to traditional nonrobust time-optimal controls for different systems. This equivalence implies that the robust time-optimal controllers must then have all the properties that are known about traditional time-optimal controllers. Further, many of the numerical methods developed for generating time-optimal commands are directly applicable to designing robust time-optimal commands.