On limitations to the achievable path tracking performance for linear multivariable plants

In this paper we consider a problem termed "path tracking". This differs from the common problem of reference tracking, in that here we can adjust the speed at which we traverse the reference trajectory. We are interested in ascertaining the degree to which we can track a given trajectory, and in characterizing the class of paths for which we can generate an appropriate temporal specification so that the path can be tracked arbitrarily well in an L₂ sense.