A state space formulation for generalized predictive control (GPC) is presented. Unlike other state space formulations, we derive both the state feedback controller and state estimator gains using a least squares framework. The present formulation provides a set of consistent design choices for both the controller and the state estimator design. It also encapsulates both single rate and multirate controllers in the same algorithm. It is argued that such a design approach can be advantageous especially when the control algorithm is required to tolerate sensor failure. The generality of the design method is illustrated by synthesizing two well-known multirate control algorithms. A link with the generalized sampled-data hold function is also established.