This paper presents some properties regarding the Multivariable Generalized Predictive Controller designed in state space. The authors proposed the design of such a controller under the condition that it gives the same results as the input-output formulation of the GPC proposed originally by Clarke. The main reason for redesigning the controller in state space is the power of the analysis tools available. These tools allow some properties to be treated more easily than under input-output formulation. These properties include: stability, robustness, closed loop representation, specifications, etc. This paper presents results related to: observability and controllability of the CARIMA model used, closed loop representation, uniqueness and the existence of control law without constraints and closed loop stability without constraints.