This work focuses on state feedback, model predictive control of particulate processes subject to asynchronous measurements. A population balance model of a typical continuous crystallizer is taken as an application example. Three controllers, i.e., a standard model predictive controller and two recently proposed Lyapunov-based model predictive controllers, are applied to stabilize the crystallizer at an open-loop, unstable steady-state in the presence of asynchronous measurements. The stability and robustness properties of the closed-loop system under the three predictive controllers are compared extensively under three different assumptions on how the measurements from the crystallizer are obtained.