The interactor matrix plays a key role in establishing multivariate performance indices for systems that are described by the superposition of linear(ized) dynamics and additive stochastic or deterministic disturbances, In this paper, new predictive interpretations for the invariant dynamics are provided. These interpretations enable bounds for the mean-square error performance to be easily and intuitively established. From these results it is shown that the number of zeros at infinity can be obtained from the formulation of a simple model predictive control problem without the requirement to explicitly form the interactor matrix. (C) 2008 Published by Elsevier Ltd.