A robust state-predictive control strategy is proposed for discrete-time multi-input/output systems with non-equal delays on signal buses. It is based on a separation property between control and prediction. The input delays are taken into account in the control law synthesis and the output delays are handled using an original steady-state Kalman predictor of order equal to the length of the state of the system without delays. Robustness, especially against uncertain delays, is improved using a state extension in the predictive gain synthesis. The classic optimal separation theorem (in the case of an one step predictor) is extended to the general case of a d + 1 step prediction for a delayed discrete-time system.