Mapping prior information onto LMI eigenvalue‐regions for discrete‐time subspace identification

Abstract

In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding linear matrix inequality (LMI) regions. In this study, first the authors 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 constrain the possible locations of the eigenvalues of the discrete-time model. Then, they show how to map the prior information onto LMI regions and, when the obtaining regions are non-convex, to obtain convex approximations.