This article investigates the antidisturbance security control for dual-rate systems that are vulnerable to unknown disturbances and denial-of-service (DoS) attacks. The asynchronous conflict resulting from sampled signals at different rates is further exacerbated by cyberattacks, rendering information estimation considerably more difficult. A new state reconstruction technique, based on alternating sampling-prediction (ASP) design, is developed. Specifically, during any fast update or and communication interruption due to an attack, a predictor is introduced to generate a virtual output. By alternating the prediction signal with the normal slow-sampling signal, an efficient state observer for reconstructing comprehensive state information is developed. Unlike traditional disturbance-observer (DO) designs that rely on measurable states, an ASP-based DO design realizes dual-rate disturbance estimation with information loss. Furthermore, by integrating state and disturbance observations, we generate a reliable control input that ensures stochastic stability of closed-loop dual-rate systems. Finally, a vision-based quadrotor landing platform and a tracking platform are constructed to serve as a typical dual-rate system. Several experiments are conducted on these platforms to verify the effectiveness of the proposed technique in handling disturbances and DoS attacks.