Abstract: This paper addresses the off-line output feedback predictive control for systems with polytopic description. An existing method first synthesizes state feedback predictive control satisfying input/state (I/S) constraints. However, in designing the state observer, the I/S constraints have not been reconsidered. This paper, on the contrary, gives the state observer a priori, and presents a set of inequalities to keep the true state, observer state and observation error within the same ellipsoid, such that I/S constraints can be dealt with by linear matrix inequalities. Based-on this idea, it off-line calculates a sequence of ellipsoids, each corresponding to a control law and an observer. The on-line real-time control law and observer are selected from the sequence, such that stability is guaranteed for the closed-loop system. The simulation example shows the effectiveness of the new technique.