Controllability and Observability of Linear Quaternion-valued Systems

Controllability and Observability of Linear Quaternion-valued Systems

The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or c...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Acta mathematica Sinica. English series 2020-11, Vol.36 (11), p.1299-1314
Hauptverfasser: Jiang, Bang Xin, Liu, Yang, Kou, Kit Ian, Wang, Zhen
Format: Artikel
Sprache:eng
Schlagworte:
Controllability
Duality theorem
Linear systems
Mathematics
Mathematics and Statistics
Observability (systems)
Quaternions
Stability
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 1314
container_issue 11
container_start_page 1299
container_title Acta mathematica Sinica. English series
container_volume 36
creator Jiang, Bang Xin
Liu, Yang
Kou, Kit Ian
Wang, Zhen
description The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or complex-valued linear systems, it is shown that the classical Caylay-Hamilton Theorem as well as Popov-Belevitch-Hautus (PBH) type controllability and observability test do not hold for linear QVS. Hence, a modified PBH type necessary condition is studied for the controllability and observability, respectively. Finally, some examples are given to illustrate the effectiveness of the obtained results.
doi_str_mv 10.1007/s10114-020-8167-1
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2473775552</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2473775552</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-a7737d37a9bdce3b2782ab45e173f5d82fc375128444d3633e662c4a40df3bfa3</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhoMoWKs_wNuC52gmn9ujlPoBhSLqOWQ3iWzZJjXZLey_d8tWPHmaYXjed-BB6BbIPRCiHjIQAI4JJbgEqTCcoRlwtsBKgjo_7aUAeYmuct4SIsSCyBlaLWPoUmxbUzVt0w2FCbbYVNmlw-8l-mLdBGdS8dabzqXQxIAPpu2dLd6H3LldvkYX3rTZ3ZzmHH0-rT6WL3i9eX5dPq5xzUB22CjFlGXKLCpbO1ZRVVJTceFAMS9sSX3NlABacs4tk4w5KWnNDSfWs8obNkd3U-8-xe_e5U5vY5_C-FJTPnYrIQQdKZioOsWck_N6n5qdSYMGoo-29GRLj7b00ZaGMUOnTB7Z8OXSX_P_oR_j62zF</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2473775552</pqid></control><display><type>article</type><title>Controllability and Observability of Linear Quaternion-valued Systems</title><source>Springer Nature - Complete Springer Journals</source><source>Alma/SFX Local Collection</source><creator>Jiang, Bang Xin ; Liu, Yang ; Kou, Kit Ian ; Wang, Zhen</creator><creatorcontrib>Jiang, Bang Xin ; Liu, Yang ; Kou, Kit Ian ; Wang, Zhen</creatorcontrib><description>The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or complex-valued linear systems, it is shown that the classical Caylay-Hamilton Theorem as well as Popov-Belevitch-Hautus (PBH) type controllability and observability test do not hold for linear QVS. Hence, a modified PBH type necessary condition is studied for the controllability and observability, respectively. Finally, some examples are given to illustrate the effectiveness of the obtained results.</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><identifier>DOI: 10.1007/s10114-020-8167-1</identifier><language>eng</language><publisher>Beijing: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</publisher><subject>Controllability ; Duality theorem ; Linear systems ; Mathematics ; Mathematics and Statistics ; Observability (systems) ; Quaternions ; Stability</subject><ispartof>Acta mathematica Sinica. English series, 2020-11, Vol.36 (11), p.1299-1314</ispartof><rights>Springer-Verlag GmbH Germany &amp; The Editorial Office of AMS 2020</rights><rights>Springer-Verlag GmbH Germany &amp; The Editorial Office of AMS 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-a7737d37a9bdce3b2782ab45e173f5d82fc375128444d3633e662c4a40df3bfa3</citedby><cites>FETCH-LOGICAL-c316t-a7737d37a9bdce3b2782ab45e173f5d82fc375128444d3633e662c4a40df3bfa3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10114-020-8167-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10114-020-8167-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,778,782,27907,27908,41471,42540,51302</link.rule.ids></links><search><creatorcontrib>Jiang, Bang Xin</creatorcontrib><creatorcontrib>Liu, Yang</creatorcontrib><creatorcontrib>Kou, Kit Ian</creatorcontrib><creatorcontrib>Wang, Zhen</creatorcontrib><title>Controllability and Observability of Linear Quaternion-valued Systems</title><title>Acta mathematica Sinica. English series</title><addtitle>Acta. Math. Sin.-English Ser</addtitle><description>The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or complex-valued linear systems, it is shown that the classical Caylay-Hamilton Theorem as well as Popov-Belevitch-Hautus (PBH) type controllability and observability test do not hold for linear QVS. Hence, a modified PBH type necessary condition is studied for the controllability and observability, respectively. Finally, some examples are given to illustrate the effectiveness of the obtained results.</description><subject>Controllability</subject><subject>Duality theorem</subject><subject>Linear systems</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Observability (systems)</subject><subject>Quaternions</subject><subject>Stability</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wNuC52gmn9ujlPoBhSLqOWQ3iWzZJjXZLey_d8tWPHmaYXjed-BB6BbIPRCiHjIQAI4JJbgEqTCcoRlwtsBKgjo_7aUAeYmuct4SIsSCyBlaLWPoUmxbUzVt0w2FCbbYVNmlw-8l-mLdBGdS8dabzqXQxIAPpu2dLd6H3LldvkYX3rTZ3ZzmHH0-rT6WL3i9eX5dPq5xzUB22CjFlGXKLCpbO1ZRVVJTceFAMS9sSX3NlABacs4tk4w5KWnNDSfWs8obNkd3U-8-xe_e5U5vY5_C-FJTPnYrIQQdKZioOsWck_N6n5qdSYMGoo-29GRLj7b00ZaGMUOnTB7Z8OXSX_P_oR_j62zF</recordid><startdate>20201101</startdate><enddate>20201101</enddate><creator>Jiang, Bang Xin</creator><creator>Liu, Yang</creator><creator>Kou, Kit Ian</creator><creator>Wang, Zhen</creator><general>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20201101</creationdate><title>Controllability and Observability of Linear Quaternion-valued Systems</title><author>Jiang, Bang Xin ; Liu, Yang ; Kou, Kit Ian ; Wang, Zhen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-a7737d37a9bdce3b2782ab45e173f5d82fc375128444d3633e662c4a40df3bfa3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Controllability</topic><topic>Duality theorem</topic><topic>Linear systems</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Observability (systems)</topic><topic>Quaternions</topic><topic>Stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jiang, Bang Xin</creatorcontrib><creatorcontrib>Liu, Yang</creatorcontrib><creatorcontrib>Kou, Kit Ian</creatorcontrib><creatorcontrib>Wang, Zhen</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Acta mathematica Sinica. English series</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jiang, Bang Xin</au><au>Liu, Yang</au><au>Kou, Kit Ian</au><au>Wang, Zhen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Controllability and Observability of Linear Quaternion-valued Systems</atitle><jtitle>Acta mathematica Sinica. English series</jtitle><stitle>Acta. Math. Sin.-English Ser</stitle><date>2020-11-01</date><risdate>2020</risdate><volume>36</volume><issue>11</issue><spage>1299</spage><epage>1314</epage><pages>1299-1314</pages><issn>1439-8516</issn><eissn>1439-7617</eissn><abstract>The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or complex-valued linear systems, it is shown that the classical Caylay-Hamilton Theorem as well as Popov-Belevitch-Hautus (PBH) type controllability and observability test do not hold for linear QVS. Hence, a modified PBH type necessary condition is studied for the controllability and observability, respectively. Finally, some examples are given to illustrate the effectiveness of the obtained results.</abstract><cop>Beijing</cop><pub>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</pub><doi>10.1007/s10114-020-8167-1</doi><tpages>16</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1439-8516
ispartof Acta mathematica Sinica. English series, 2020-11, Vol.36 (11), p.1299-1314
issn 1439-8516
1439-7617
language eng
recordid cdi_proquest_journals_2473775552
source Springer Nature - Complete Springer Journals; Alma/SFX Local Collection
subjects Controllability
Duality theorem
Linear systems
Mathematics
Mathematics and Statistics
Observability (systems)
Quaternions
Stability
title Controllability and Observability of Linear Quaternion-valued Systems
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T17%3A24%3A44IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Controllability%20and%20Observability%20of%20Linear%20Quaternion-valued%20Systems&rft.jtitle=Acta%20mathematica%20Sinica.%20English%20series&rft.au=Jiang,%20Bang%20Xin&rft.date=2020-11-01&rft.volume=36&rft.issue=11&rft.spage=1299&rft.epage=1314&rft.pages=1299-1314&rft.issn=1439-8516&rft.eissn=1439-7617&rft_id=info:doi/10.1007/s10114-020-8167-1&rft_dat=%3Cproquest_cross%3E2473775552%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2473775552&rft_id=info:pmid/&rfr_iscdi=true