A model predictive control (MPC) technique is developed for systems with measurements available at different sampling rates. The method uses general state-space system representations that incorporate secondary measurements as well as primary measurements. The optimal multi-rate (MR) filtering method is used to develop prediction equations for MPC. A simple suboptimal cascade filter is also proposed for dual-rate (DR) systems where the primary measurements are available at a 'slow’ rate and the secondary measurements are available at a 'fast’ rate. In addition to significant reduction in filter-gain computation requirements, the suboptimal filtering strategy offers superior primary-measurement-failure tolerance. The applicability of the proposed methods to realistic systems is demonstrated through an example application to a high-purity distillation column.