A supervisor has a robustness in the sense that it achieves the desirable behavior for more than one discrete event system in general. This robustness is useful when a supervisor controls the system with model uncertainty. This paper studies the robust finite state supervisor in the case that the desirable behavior is specified as a closed language. Given an arbitrary supervisor, we characterize all systems for which the desirable behavior is achieved by the supervisor. By using this characterization, we show that there exists the robust finite state supervisor which maximizes the class of systems for which the supervisor achieves the desirable behavior.