Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form

We study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewise-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decompo...

Full description

Saved in:
Bibliographic Details
Published in:IEEE control systems letters 2024-01, Vol.8, p.1841-1846
Main Authors: Rouphael, Elie, Mejari, Manas, Petreczky, Mihaly, Belkoura, Lotfi
Format: Article
Language:English
Subjects:
Automatic
Engineering Sciences
innovation representation
Linear systems
Stochastic processes
stochastic realization theory
Switched systems
Switches
System identification
Technological innovation
White noise
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c227t-c4ad3693c8287d184c97ae0f6d5db2cecd03716f72f7367ab6eb5320ff872edd3
container_end_page 1846
container_issue
container_start_page 1841
container_title IEEE control systems letters
container_volume 8
creator Rouphael, Elie
Mejari, Manas
Petreczky, Mihaly
Belkoura, Lotfi
description We study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewise-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decomposition, we show existence of state-space representation in innovation form, and we provide sufficient conditions for such representations to be minimal and unique up to isomorphism.
doi_str_mv 10.1109/LCSYS.2024.3417189
format article
fullrecord <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_04787641v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>10565856</ieee_id><sourcerecordid>oai_HAL_hal_04787641v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c227t-c4ad3693c8287d184c97ae0f6d5db2cecd03716f72f7367ab6eb5320ff872edd3</originalsourceid><addsrcrecordid>eNpNUU2L2zAQNUsLG3b3D5QedO0hqSTbkt1bSPcjYFioE0pPRpFGWCWWUklJmv19-8PWdpYlp5l5896bgZckXwieEYLL79Wi_lPPKKbZLM0IJ0V5lUxoxvMpyXL26aK_Tu5C-IsxJgXlmJaT5HXljsIrVEcnWxGikegXiK15EdE4i1YtOH9C2nn0CBb8sAGFKmNBeFQfTZRtP9enEKEL6LeJLVra3T6GH-gnSNftXDCj09JGd3lFWNUzIvjOWDMii4FtwcYwLu__9zBYCeO0tubfvv8gBOR0b2bd4fzhg_PdbfJZi22Au_d6k6wf7leLp2n1_LhczKuppJTHqcyESlmZyoIWXJEikyUXgDVTudpQCVLhlBOmOdU8ZVxsGGzylGKtC05BqfQm-Xb2bcW22XnTCX9qnDDN07xqBgxnvOAsIwfSc-mZK70LwYP-EBDcDLE1Y2zNEFvzHlsv-noWGQC4EOQsL3KWvgFG_pmp</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form</title><source>IEEE Electronic Library (IEL) Journals</source><creator>Rouphael, Elie ; Mejari, Manas ; Petreczky, Mihaly ; Belkoura, Lotfi</creator><creatorcontrib>Rouphael, Elie ; Mejari, Manas ; Petreczky, Mihaly ; Belkoura, Lotfi</creatorcontrib><description>We study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewise-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decomposition, we show existence of state-space representation in innovation form, and we provide sufficient conditions for such representations to be minimal and unique up to isomorphism.</description><identifier>ISSN: 2475-1456</identifier><identifier>EISSN: 2475-1456</identifier><identifier>DOI: 10.1109/LCSYS.2024.3417189</identifier><identifier>CODEN: ICSLBO</identifier><language>eng</language><publisher>IEEE</publisher><subject>Automatic ; Engineering Sciences ; innovation representation ; Linear systems ; Stochastic processes ; stochastic realization theory ; Switched systems ; Switches ; System identification ; Technological innovation ; White noise</subject><ispartof>IEEE control systems letters, 2024-01, Vol.8, p.1841-1846</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c227t-c4ad3693c8287d184c97ae0f6d5db2cecd03716f72f7367ab6eb5320ff872edd3</cites><orcidid>0000-0003-2264-5689 ; 0009-0005-7818-1272 ; 0000-0003-3455-942X ; 0000-0002-0641-1156</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/10565856$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>230,314,776,780,881,27903,27904,54774</link.rule.ids><backlink>$$Uhttps://hal.science/hal-04787641$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Rouphael, Elie</creatorcontrib><creatorcontrib>Mejari, Manas</creatorcontrib><creatorcontrib>Petreczky, Mihaly</creatorcontrib><creatorcontrib>Belkoura, Lotfi</creatorcontrib><title>Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form</title><title>IEEE control systems letters</title><addtitle>LCSYS</addtitle><description>We study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewise-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decomposition, we show existence of state-space representation in innovation form, and we provide sufficient conditions for such representations to be minimal and unique up to isomorphism.</description><subject>Automatic</subject><subject>Engineering Sciences</subject><subject>innovation representation</subject><subject>Linear systems</subject><subject>Stochastic processes</subject><subject>stochastic realization theory</subject><subject>Switched systems</subject><subject>Switches</subject><subject>System identification</subject><subject>Technological innovation</subject><subject>White noise</subject><issn>2475-1456</issn><issn>2475-1456</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNpNUU2L2zAQNUsLG3b3D5QedO0hqSTbkt1bSPcjYFioE0pPRpFGWCWWUklJmv19-8PWdpYlp5l5896bgZckXwieEYLL79Wi_lPPKKbZLM0IJ0V5lUxoxvMpyXL26aK_Tu5C-IsxJgXlmJaT5HXljsIrVEcnWxGikegXiK15EdE4i1YtOH9C2nn0CBb8sAGFKmNBeFQfTZRtP9enEKEL6LeJLVra3T6GH-gnSNftXDCj09JGd3lFWNUzIvjOWDMii4FtwcYwLu__9zBYCeO0tubfvv8gBOR0b2bd4fzhg_PdbfJZi22Au_d6k6wf7leLp2n1_LhczKuppJTHqcyESlmZyoIWXJEikyUXgDVTudpQCVLhlBOmOdU8ZVxsGGzylGKtC05BqfQm-Xb2bcW22XnTCX9qnDDN07xqBgxnvOAsIwfSc-mZK70LwYP-EBDcDLE1Y2zNEFvzHlsv-noWGQC4EOQsL3KWvgFG_pmp</recordid><startdate>20240101</startdate><enddate>20240101</enddate><creator>Rouphael, Elie</creator><creator>Mejari, Manas</creator><creator>Petreczky, Mihaly</creator><creator>Belkoura, Lotfi</creator><general>IEEE</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0003-2264-5689</orcidid><orcidid>https://orcid.org/0009-0005-7818-1272</orcidid><orcidid>https://orcid.org/0000-0003-3455-942X</orcidid><orcidid>https://orcid.org/0000-0002-0641-1156</orcidid></search><sort><creationdate>20240101</creationdate><title>Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form</title><author>Rouphael, Elie ; Mejari, Manas ; Petreczky, Mihaly ; Belkoura, Lotfi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c227t-c4ad3693c8287d184c97ae0f6d5db2cecd03716f72f7367ab6eb5320ff872edd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Automatic</topic><topic>Engineering Sciences</topic><topic>innovation representation</topic><topic>Linear systems</topic><topic>Stochastic processes</topic><topic>stochastic realization theory</topic><topic>Switched systems</topic><topic>Switches</topic><topic>System identification</topic><topic>Technological innovation</topic><topic>White noise</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rouphael, Elie</creatorcontrib><creatorcontrib>Mejari, Manas</creatorcontrib><creatorcontrib>Petreczky, Mihaly</creatorcontrib><creatorcontrib>Belkoura, Lotfi</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998–Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>IEEE control systems letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rouphael, Elie</au><au>Mejari, Manas</au><au>Petreczky, Mihaly</au><au>Belkoura, Lotfi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form</atitle><jtitle>IEEE control systems letters</jtitle><stitle>LCSYS</stitle><date>2024-01-01</date><risdate>2024</risdate><volume>8</volume><spage>1841</spage><epage>1846</epage><pages>1841-1846</pages><issn>2475-1456</issn><eissn>2475-1456</eissn><coden>ICSLBO</coden><abstract>We study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewise-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decomposition, we show existence of state-space representation in innovation form, and we provide sufficient conditions for such representations to be minimal and unique up to isomorphism.</abstract><pub>IEEE</pub><doi>10.1109/LCSYS.2024.3417189</doi><tpages>6</tpages><orcidid>https://orcid.org/0000-0003-2264-5689</orcidid><orcidid>https://orcid.org/0009-0005-7818-1272</orcidid><orcidid>https://orcid.org/0000-0003-3455-942X</orcidid><orcidid>https://orcid.org/0000-0002-0641-1156</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2475-1456
ispartof IEEE control systems letters, 2024-01, Vol.8, p.1841-1846
issn 2475-1456
2475-1456
language eng
recordid cdi_hal_primary_oai_HAL_hal_04787641v1
source IEEE Electronic Library (IEL) Journals
subjects Automatic
Engineering Sciences
innovation representation
Linear systems
Stochastic processes
stochastic realization theory
Switched systems
Switches
System identification
Technological innovation
White noise
title Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-24T09%3A36%3A41IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Toward%20Stochastic%20Realization%20Theory%20for%20Generalized%20Linear%20Switched%20Systems%20With%20Inputs:%20Decomposition%20Into%20Stochastic%20and%20Deterministic%20Components%20and%20Existence%20and%20Uniqueness%20of%20Innovation%20Form&rft.jtitle=IEEE%20control%20systems%20letters&rft.au=Rouphael,%20Elie&rft.date=2024-01-01&rft.volume=8&rft.spage=1841&rft.epage=1846&rft.pages=1841-1846&rft.issn=2475-1456&rft.eissn=2475-1456&rft.coden=ICSLBO&rft_id=info:doi/10.1109/LCSYS.2024.3417189&rft_dat=%3Chal_cross%3Eoai_HAL_hal_04787641v1%3C/hal_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c227t-c4ad3693c8287d184c97ae0f6d5db2cecd03716f72f7367ab6eb5320ff872edd3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_ieee_id=10565856&rfr_iscdi=true