A framework called generalized inferential control (GIC) is established for designing robust, linear inferential control systems for multi-rate sampled-data systems. Practical issues such as model/plant mismatch, constraints, and actuator/measurement failure tolerance are addressed rigorously in the GIC framework. Various H2-optimal design techniques such as linear quadratic Gaussian (LQG), model-predictive control (MPC), and internal model control (IMC) are discussed and extended in the context of GIC. In addition, a connection between MPC and IMC is established and a method for replacing the