  In subspace identification, prior information can be used to constrain the
eigenvalues of the estimated state-space model by defining corresponding LMI
regions. In this paper, first we argue on what kind of practical information
can be extracted from historical data or step-response experiments to possibly
improve the dynamical properties of the corresponding model and, also, on how
to mitigate the effect of the uncertainty on such information. For instance,
prior knowledge regarding the overshoot, the period between damped oscillations
and settling time may be useful to constraint the possible locations of the
eigenvalues of the discrete-time model. Then, we show how to map the prior
information onto LMI regions and, when the obtaining regions are non-convex, to
obtain convex approximations.
