Beyond the fundamental lemma: from finite time series to linear system

TL;DR

This paper establishes precise conditions to uniquely identify a minimal linear time-invariant system from finite data, considering bounds on lag and state dimension, advancing system identification methods.

Contribution

It provides necessary and sufficient conditions for unique system identification from finite data with bounds on lag and state dimension.

Findings

Derived conditions for unique identification of linear systems.

Applicable to systems with bounded lag and state space dimensions.

Enhances understanding of finite data system identification.

Abstract

We state necessary and sufficient conditions to uniquely identify (modulo state isomorphism) a linear time-invariant minimal input-state-output system from finite input-output data and upper- and lower bounds on lag and state space dimension.