Polynomials‐based summation inequalities and their applications to discrete‐time systems with time‐varying delays
Summary This paper proposes a novel summation inequality, say a polynomials‐based summation inequality, which contains well‐known summation inequalities as special cases. By specially choosing slack matrices, polynomial functions, and an arbitrary vector, it reduces to Moon's inequality, a disc...
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| Veröffentlicht in: | International journal of robust and nonlinear control 2017-11, Vol.27 (17), p.3604-3619 |
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| container_issue | 17 |
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| container_title | International journal of robust and nonlinear control |
| container_volume | 27 |
| creator | Lee, Seok Young Lee, Won Il Park, PooGyeon |
| description | Summary
This paper proposes a novel summation inequality, say a polynomials‐based summation inequality, which contains well‐known summation inequalities as special cases. By specially choosing slack matrices, polynomial functions, and an arbitrary vector, it reduces to Moon's inequality, a discrete‐time counterpart of Wirtinger‐based integral inequality, auxiliary function‐based summation inequalities employing the same‐order orthogonal polynomial functions. Thus, the proposed summation inequality is more general than other summation inequalities. Additionally, this paper derives the polynomials‐based summation inequality employing first‐order and second‐order orthogonal polynomial functions, which contributes to obtaining improved stability criteria for discrete‐time systems with time‐varying delays. Copyright © 2017 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/rnc.3755 |
| format | Article |
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This paper proposes a novel summation inequality, say a polynomials‐based summation inequality, which contains well‐known summation inequalities as special cases. By specially choosing slack matrices, polynomial functions, and an arbitrary vector, it reduces to Moon's inequality, a discrete‐time counterpart of Wirtinger‐based integral inequality, auxiliary function‐based summation inequalities employing the same‐order orthogonal polynomial functions. Thus, the proposed summation inequality is more general than other summation inequalities. Additionally, this paper derives the polynomials‐based summation inequality employing first‐order and second‐order orthogonal polynomial functions, which contributes to obtaining improved stability criteria for discrete‐time systems with time‐varying delays. Copyright © 2017 John Wiley & Sons, Ltd.</description><identifier>ISSN: 1049-8923</identifier><identifier>EISSN: 1099-1239</identifier><identifier>DOI: 10.1002/rnc.3755</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>Discrete time systems ; discrete‐time system, linear matrix inequality (LMI) ; Functions (mathematics) ; Inequalities ; Inequality ; Lyapunov–Krasovskii functional ; Mathematical analysis ; Matrix algebra ; Matrix methods ; Polynomials ; stability analysis ; Stability criteria ; summation inequality ; time‐varying delay</subject><ispartof>International journal of robust and nonlinear control, 2017-11, Vol.27 (17), p.3604-3619</ispartof><rights>Copyright © 2017 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3305-c99b2c522af76c681f997f0d94fb01f7b3218697c11c255c0373e91df70dae313</citedby><cites>FETCH-LOGICAL-c3305-c99b2c522af76c681f997f0d94fb01f7b3218697c11c255c0373e91df70dae313</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Frnc.3755$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Frnc.3755$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27903,27904,45553,45554</link.rule.ids></links><search><creatorcontrib>Lee, Seok Young</creatorcontrib><creatorcontrib>Lee, Won Il</creatorcontrib><creatorcontrib>Park, PooGyeon</creatorcontrib><title>Polynomials‐based summation inequalities and their applications to discrete‐time systems with time‐varying delays</title><title>International journal of robust and nonlinear control</title><description>Summary
This paper proposes a novel summation inequality, say a polynomials‐based summation inequality, which contains well‐known summation inequalities as special cases. By specially choosing slack matrices, polynomial functions, and an arbitrary vector, it reduces to Moon's inequality, a discrete‐time counterpart of Wirtinger‐based integral inequality, auxiliary function‐based summation inequalities employing the same‐order orthogonal polynomial functions. Thus, the proposed summation inequality is more general than other summation inequalities. Additionally, this paper derives the polynomials‐based summation inequality employing first‐order and second‐order orthogonal polynomial functions, which contributes to obtaining improved stability criteria for discrete‐time systems with time‐varying delays. Copyright © 2017 John Wiley & Sons, Ltd.</description><subject>Discrete time systems</subject><subject>discrete‐time system, linear matrix inequality (LMI)</subject><subject>Functions (mathematics)</subject><subject>Inequalities</subject><subject>Inequality</subject><subject>Lyapunov–Krasovskii functional</subject><subject>Mathematical analysis</subject><subject>Matrix algebra</subject><subject>Matrix methods</subject><subject>Polynomials</subject><subject>stability analysis</subject><subject>Stability criteria</subject><subject>summation inequality</subject><subject>time‐varying delay</subject><issn>1049-8923</issn><issn>1099-1239</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KxDAUhYMoOI6CjxBw46ZjftqmWcrgHwwqouuQpomToX8mqUN3PoLP6JOYzrh1dS_3fJxzOQCcY7TACJEr16oFZVl2AGYYcZ5gQvnhtKc8KTihx-DE-w1CUSPpDGyfu3psu8bK2v98fZfS6wr6oWlksF0Lbas_BlnbYLWHsq1gWGvroOz72qod4mHoYGW9cjro6BBso6EffdCNh1sb1nC6ROFTutG277DStRz9KTgyMVKf_c05eLu9eV3eJ6unu4fl9SpRlKIsUZyXRGWESMNylRfYcM4MqnhqSoQNKynBRc6ZwliRLFOIMqo5rgxDldQU0zm42Pv2rvsYtA9i0w2ujZEC8zzNUlTkLFKXe0q5znunjeidbeLDAiMx1SpirWKqNaLJHt3aWo__cuLlcbnjfwFxnH53</recordid><startdate>20171125</startdate><enddate>20171125</enddate><creator>Lee, Seok Young</creator><creator>Lee, Won Il</creator><creator>Park, PooGyeon</creator><general>John Wiley & Sons, Ltd</general><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20171125</creationdate><title>Polynomials‐based summation inequalities and their applications to discrete‐time systems with time‐varying delays</title><author>Lee, Seok Young ; Lee, Won Il ; Park, PooGyeon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3305-c99b2c522af76c681f997f0d94fb01f7b3218697c11c255c0373e91df70dae313</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Discrete time systems</topic><topic>discrete‐time system, linear matrix inequality (LMI)</topic><topic>Functions (mathematics)</topic><topic>Inequalities</topic><topic>Inequality</topic><topic>Lyapunov–Krasovskii functional</topic><topic>Mathematical analysis</topic><topic>Matrix algebra</topic><topic>Matrix methods</topic><topic>Polynomials</topic><topic>stability analysis</topic><topic>Stability criteria</topic><topic>summation inequality</topic><topic>time‐varying delay</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lee, Seok Young</creatorcontrib><creatorcontrib>Lee, Won Il</creatorcontrib><creatorcontrib>Park, PooGyeon</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</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>International journal of robust and nonlinear control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lee, Seok Young</au><au>Lee, Won Il</au><au>Park, PooGyeon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Polynomials‐based summation inequalities and their applications to discrete‐time systems with time‐varying delays</atitle><jtitle>International journal of robust and nonlinear control</jtitle><date>2017-11-25</date><risdate>2017</risdate><volume>27</volume><issue>17</issue><spage>3604</spage><epage>3619</epage><pages>3604-3619</pages><issn>1049-8923</issn><eissn>1099-1239</eissn><abstract>Summary
This paper proposes a novel summation inequality, say a polynomials‐based summation inequality, which contains well‐known summation inequalities as special cases. By specially choosing slack matrices, polynomial functions, and an arbitrary vector, it reduces to Moon's inequality, a discrete‐time counterpart of Wirtinger‐based integral inequality, auxiliary function‐based summation inequalities employing the same‐order orthogonal polynomial functions. Thus, the proposed summation inequality is more general than other summation inequalities. Additionally, this paper derives the polynomials‐based summation inequality employing first‐order and second‐order orthogonal polynomial functions, which contributes to obtaining improved stability criteria for discrete‐time systems with time‐varying delays. Copyright © 2017 John Wiley & Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/rnc.3755</doi><tpages>16</tpages></addata></record> |
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| ispartof | International journal of robust and nonlinear control, 2017-11, Vol.27 (17), p.3604-3619 |
| issn | 1049-8923 1099-1239 |
| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Discrete time systems discrete‐time system, linear matrix inequality (LMI) Functions (mathematics) Inequalities Inequality Lyapunov–Krasovskii functional Mathematical analysis Matrix algebra Matrix methods Polynomials stability analysis Stability criteria summation inequality time‐varying delay |
| title | Polynomials‐based summation inequalities and their applications to discrete‐time systems with time‐varying delays |
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