The design of stabilizing predictive controllers for stochastic discrete-time linear plants is formulated in a state-space framework. The resulting approach, named SSPC (Stabilizing Stochastic Predictive Control), extends straightforwardly to MIMO plants wherein the controlled output is not directly measurable. It is demonstrated that SSPC leads to well known input-output solutions, such as SIORHC (Stabilizing Input/Output Receding Horizon Control) or SGPC (Stable Generalized Predictive Control), when particular state-space realizations of a CARIMA model are adopted. An efficient algorithm for computing the SSPC control law is also presented.