A note on persistency of excitation

JC Willems; P Rapisarda; null Markovsky; BLM De Moor

doi:10.1016/j.sysconle.2004.09.003

A note on persistency of excitation

JC Willems, P Rapisarda, Markovsky^*, BLM De Moor

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

219 Citations (Web of Science)

Abstract

We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full system behavior. This is then applied to obtain conditions under which the state trajectory of a state representation spans the whole state space. The related question of when the matrix formed from a state sequence has linearly independent rows from the matrix formed from an input sequence and a finite number of its shifts is of central importance in subspace system identification. (C) 2004 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	325-329
Number of pages	5
Journal	Systems & Control Letters
Volume	54
Issue number	4
DOIs	https://doi.org/10.1016/j.sysconle.2004.09.003
Publication status	Published - Apr 2005

Keywords

bahavioral systems
persistency of excitation
lags
annihilators
system identification
TIME-INVARIANT SYSTEMS
LINEAR-SYSTEM
IDENTIFICATION

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10.1016/j.sysconle.2004.09.003

Cite this

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title = "A note on persistency of excitation",

abstract = "We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full system behavior. This is then applied to obtain conditions under which the state trajectory of a state representation spans the whole state space. The related question of when the matrix formed from a state sequence has linearly independent rows from the matrix formed from an input sequence and a finite number of its shifts is of central importance in subspace system identification. (C) 2004 Elsevier B.V. All rights reserved.",

keywords = "bahavioral systems, persistency of excitation, lags, annihilators, system identification, TIME-INVARIANT SYSTEMS, LINEAR-SYSTEM, IDENTIFICATION",

author = "JC Willems and P Rapisarda and Markovsky and {De Moor}, BLM",

year = "2005",

month = apr,

doi = "10.1016/j.sysconle.2004.09.003",

language = "English",

volume = "54",

pages = "325--329",

journal = "Systems & Control Letters",

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publisher = "Elsevier Science",

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TY - JOUR

T1 - A note on persistency of excitation

AU - Willems, JC

AU - Rapisarda, P

AU - Markovsky, null

AU - De Moor, BLM

PY - 2005/4

Y1 - 2005/4

N2 - We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full system behavior. This is then applied to obtain conditions under which the state trajectory of a state representation spans the whole state space. The related question of when the matrix formed from a state sequence has linearly independent rows from the matrix formed from an input sequence and a finite number of its shifts is of central importance in subspace system identification. (C) 2004 Elsevier B.V. All rights reserved.

AB - We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full system behavior. This is then applied to obtain conditions under which the state trajectory of a state representation spans the whole state space. The related question of when the matrix formed from a state sequence has linearly independent rows from the matrix formed from an input sequence and a finite number of its shifts is of central importance in subspace system identification. (C) 2004 Elsevier B.V. All rights reserved.

KW - bahavioral systems

KW - persistency of excitation

KW - lags

KW - annihilators

KW - system identification

KW - TIME-INVARIANT SYSTEMS

KW - LINEAR-SYSTEM

KW - IDENTIFICATION

U2 - 10.1016/j.sysconle.2004.09.003

DO - 10.1016/j.sysconle.2004.09.003

M3 - Article

SN - 0167-6911

VL - 54

SP - 325

EP - 329

JO - Systems & Control Letters

JF - Systems & Control Letters

IS - 4

ER -