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

## TL;DR

This paper presents a method to incorporate prior information into discrete-time subspace identification by mapping it onto LMI eigenvalue regions, improving model properties while handling uncertainties.

## Contribution

It introduces a systematic approach to translate practical prior knowledge into convex LMI regions for eigenvalue constraints in subspace identification.

## Key findings

- Effective mapping of prior info onto LMI regions
- Convex approximations for non-convex eigenvalue regions
- Enhanced control over model eigenvalue placement

## Abstract

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.