In this paper, the asymptotic properties of tracking systems incorporating linear multivariable plants which are amenable to fast-sampling error-actuated control (Bradshaw and Porter 1980) are characterized in terms of the eigenstructure of the closed-loop plant matrices. It is shown that the closed-loop eigenstructure is such that the tracking behaviour of systems incorporating fast-sampling error-actuated controllers designed in accordance with the synthesis technique of Bradshaw and Porter (1980) is increasingly dominated by the modes associated with characteristic roots of the form λ=l+σ as the sampling frequency is increased and that increasingly ‘tight’ control is therefore achieved. These theoretical results are illustrated in the case of a closed-loop system incorporating a third-order plant and a fast-sampling error-actuated controller by the presentation of the computed closed-loop eigenstructure and of the results of computer simulation studies.