A class of dual-rate sampled-data systems is considered, where the sampling rate is asynchronously related to the rate at which the hold element is operating. Such asynchronous sampled-data systems are aperiodic, and hence the lifting technique, which is used to represent synchronous sampled-data systems as single-rate discrete systems, cannot be applied to the asynchronous case. In this study, optimal H-infinity and LQG controllers for asynchronous sampled-data systems are derived using a two-Riccati equation approach, which does not rely on the lifting method. A distribution theorem is used to evaluate the optimal stationary performance levels in the two cases.