A Criterion for Hurwitz Polynomials and its Applications
We present a new criterion to determine the stability of polynomial with real coefficients. Combing with the existing results of the real and negative roots discrimination, we deduced the explicit conditions of stability for any real polynomial with a degree no more than four. Meanwhile, we discusse...
Gespeichert in:
| Veröffentlicht in: | International journal of modern education and computer science 2011-02, Vol.3 (1), p.38-44 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 44 |
|---|---|
| container_issue | 1 |
| container_start_page | 38 |
| container_title | International journal of modern education and computer science |
| container_volume | 3 |
| creator | Xie, Liejun |
| description | We present a new criterion to determine the stability of polynomial with real coefficients. Combing with the existing results of the real and negative roots discrimination, we deduced the explicit conditions of stability for any real polynomial with a degree no more than four. Meanwhile, we discussed the problem of controls system stability and inertia of Bezout matrix as the applications of the criterion. A necessary and sufficient condition to determine the stability of the characteristic polynomial of the continuous time control systems was proposed. And also, we discussed a pathological case of the bilinear transformation, which can convert the stability analysis of a given discrete time system to the corresponding continuous time system, and brought forward an alternative one. |
| doi_str_mv | 10.5815/ijmecs.2011.01.06 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1627740472</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3506696911</sourcerecordid><originalsourceid>FETCH-LOGICAL-c1616-7623f8d4650c9d7870d3c2c2f922aae0e79e17511ee5f085abae1486074f78783</originalsourceid><addsrcrecordid>eNo9kE9LAzEQxYMoWGo_gLeA560z2c2fPZaiVijoQcFbiNkEUtrNmuwi9dObUnF4MA_mxzx4hNwiLLlCfh92B2fzkgHiEorEBZkxkLwClB-X_17gNVnkvIMyom0YtDOiVnSdwuhSiD31MdHNlL7D-ENf4_7Yx0Mw-0xN39EwZroahn2wZixsviFXvtzc4m_Pyfvjw9t6U21fnp7Xq21lS56opGC1V10jONi2k0pCV1tmmW8ZM8aBk61DyRGd4x4UN5_GYaMEyMYXWtVzcnf-O6T4Nbk86l2cUl8iNQomZQONZIXCM2VTzDk5r4cUDiYdNYI-daTPHelTRxqKRP0Le81ZoA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1627740472</pqid></control><display><type>article</type><title>A Criterion for Hurwitz Polynomials and its Applications</title><source>EZB-FREE-00999 freely available EZB journals</source><creator>Xie, Liejun</creator><creatorcontrib>Xie, Liejun</creatorcontrib><description>We present a new criterion to determine the stability of polynomial with real coefficients. Combing with the existing results of the real and negative roots discrimination, we deduced the explicit conditions of stability for any real polynomial with a degree no more than four. Meanwhile, we discussed the problem of controls system stability and inertia of Bezout matrix as the applications of the criterion. A necessary and sufficient condition to determine the stability of the characteristic polynomial of the continuous time control systems was proposed. And also, we discussed a pathological case of the bilinear transformation, which can convert the stability analysis of a given discrete time system to the corresponding continuous time system, and brought forward an alternative one.</description><identifier>ISSN: 2075-0161</identifier><identifier>EISSN: 2075-017X</identifier><identifier>DOI: 10.5815/ijmecs.2011.01.06</identifier><language>eng</language><publisher>Hong Kong: Modern Education and Computer Science Press</publisher><subject>Algebra ; Algorithms ; Computer science ; Polynomials ; Systems stability</subject><ispartof>International journal of modern education and computer science, 2011-02, Vol.3 (1), p.38-44</ispartof><rights>Copyright Modern Education and Computer Science Press Feb 2011</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c1616-7623f8d4650c9d7870d3c2c2f922aae0e79e17511ee5f085abae1486074f78783</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27922,27923</link.rule.ids></links><search><creatorcontrib>Xie, Liejun</creatorcontrib><title>A Criterion for Hurwitz Polynomials and its Applications</title><title>International journal of modern education and computer science</title><description>We present a new criterion to determine the stability of polynomial with real coefficients. Combing with the existing results of the real and negative roots discrimination, we deduced the explicit conditions of stability for any real polynomial with a degree no more than four. Meanwhile, we discussed the problem of controls system stability and inertia of Bezout matrix as the applications of the criterion. A necessary and sufficient condition to determine the stability of the characteristic polynomial of the continuous time control systems was proposed. And also, we discussed a pathological case of the bilinear transformation, which can convert the stability analysis of a given discrete time system to the corresponding continuous time system, and brought forward an alternative one.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Computer science</subject><subject>Polynomials</subject><subject>Systems stability</subject><issn>2075-0161</issn><issn>2075-017X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNo9kE9LAzEQxYMoWGo_gLeA560z2c2fPZaiVijoQcFbiNkEUtrNmuwi9dObUnF4MA_mxzx4hNwiLLlCfh92B2fzkgHiEorEBZkxkLwClB-X_17gNVnkvIMyom0YtDOiVnSdwuhSiD31MdHNlL7D-ENf4_7Yx0Mw-0xN39EwZroahn2wZixsviFXvtzc4m_Pyfvjw9t6U21fnp7Xq21lS56opGC1V10jONi2k0pCV1tmmW8ZM8aBk61DyRGd4x4UN5_GYaMEyMYXWtVzcnf-O6T4Nbk86l2cUl8iNQomZQONZIXCM2VTzDk5r4cUDiYdNYI-daTPHelTRxqKRP0Le81ZoA</recordid><startdate>20110208</startdate><enddate>20110208</enddate><creator>Xie, Liejun</creator><general>Modern Education and Computer Science Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>0-V</scope><scope>3V.</scope><scope>7XB</scope><scope>88B</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ALSLI</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BVBZV</scope><scope>CCPQU</scope><scope>CJNVE</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>M0N</scope><scope>M0P</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEDU</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>Q9U</scope></search><sort><creationdate>20110208</creationdate><title>A Criterion for Hurwitz Polynomials and its Applications</title><author>Xie, Liejun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1616-7623f8d4650c9d7870d3c2c2f922aae0e79e17511ee5f085abae1486074f78783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Computer science</topic><topic>Polynomials</topic><topic>Systems stability</topic><toplevel>online_resources</toplevel><creatorcontrib>Xie, Liejun</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Social Sciences Premium Collection</collection><collection>ProQuest Central (Corporate)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Education Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Social Science Premium Collection</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>East & South Asia Database</collection><collection>ProQuest One Community College</collection><collection>Education Collection</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Computing Database</collection><collection>Education Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Education</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>ProQuest Central Basic</collection><jtitle>International journal of modern education and computer science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xie, Liejun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Criterion for Hurwitz Polynomials and its Applications</atitle><jtitle>International journal of modern education and computer science</jtitle><date>2011-02-08</date><risdate>2011</risdate><volume>3</volume><issue>1</issue><spage>38</spage><epage>44</epage><pages>38-44</pages><issn>2075-0161</issn><eissn>2075-017X</eissn><abstract>We present a new criterion to determine the stability of polynomial with real coefficients. Combing with the existing results of the real and negative roots discrimination, we deduced the explicit conditions of stability for any real polynomial with a degree no more than four. Meanwhile, we discussed the problem of controls system stability and inertia of Bezout matrix as the applications of the criterion. A necessary and sufficient condition to determine the stability of the characteristic polynomial of the continuous time control systems was proposed. And also, we discussed a pathological case of the bilinear transformation, which can convert the stability analysis of a given discrete time system to the corresponding continuous time system, and brought forward an alternative one.</abstract><cop>Hong Kong</cop><pub>Modern Education and Computer Science Press</pub><doi>10.5815/ijmecs.2011.01.06</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2075-0161 |
| ispartof | International journal of modern education and computer science, 2011-02, Vol.3 (1), p.38-44 |
| issn | 2075-0161 2075-017X |
| language | eng |
| recordid | cdi_proquest_journals_1627740472 |
| source | EZB-FREE-00999 freely available EZB journals |
| subjects | Algebra Algorithms Computer science Polynomials Systems stability |
| title | A Criterion for Hurwitz Polynomials and its Applications |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T11%3A44%3A48IST&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=A%20Criterion%20for%20Hurwitz%20Polynomials%20and%20its%20Applications&rft.jtitle=International%20journal%20of%20modern%20education%20and%20computer%20science&rft.au=Xie,%20Liejun&rft.date=2011-02-08&rft.volume=3&rft.issue=1&rft.spage=38&rft.epage=44&rft.pages=38-44&rft.issn=2075-0161&rft.eissn=2075-017X&rft_id=info:doi/10.5815/ijmecs.2011.01.06&rft_dat=%3Cproquest_cross%3E3506696911%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=1627740472&rft_id=info:pmid/&rfr_iscdi=true |