Abstract: A time-minimum robust time delay filter of flexible system is proposed in this paper to improve the robustness of traditional time-optimal control. It is shown that several time-minimum robust time delay filters are equivalent to traditional non-robust time-optimal controls for augmented systems. This equivalence implies that sufficient conditions from traditional time optimal control provide a method to verify whether numerical solutions of time-minimum robust time delay filter are indeed the optimum. The simulation results demonstrate the key results.