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Beyond the Fundamental Lemma: From Finite Time Series to Linear System

Authors
M. Kanat Camlibel, Paolo Rapisarda
Year
2024
Preprint
Algorithm
Finite Time Series Realization Conditions
Source
arXiv
Identifiers
arXiv 2405.18962

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.

Summary

Revisits what can be identified from finite input-output time series beyond the trajectory-spanning statement of the fundamental lemma. The paper gives exact identifiability conditions and dimension/lag bounds, making it a more system-identification-oriented complement to direct control results.

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Tags

Behavioral systems System identification Fundamental lemma Linear systems Finite time series Minimal realization Lag bounds Input-output data

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