Abstract: This article puts forward a kind of asynchronous multirate sampled-data system. Aiming at the difficulties in analyzing and designing this kind of asynchronous systems, we investigate the continuity property of its'close-loop performance on the time-delay of sampler and hold. The results have shown that its close-loop performance is continuous function of the time delay. According to the continuity property, the aperiodic asynchronous multirate system can be approximated by a periodic asynchronous multirate system by any given accuracy under few changes in performance of the system, then we can deal with them using the known the methods.