Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties
This paper addresses the problem of robust stability for quaternion-valued neural networks (QVNNs) with leakage delay, discrete delay and parameter uncertainties. Based on Homeomorphic mapping theorem and Lyapunov theorem, via modulus inequality technique of quaternions, some sufficient conditions o...
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| Veröffentlicht in: | Neural networks 2017-07, Vol.91, p.55-65 |
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| container_title | Neural networks |
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| creator | Chen, Xiaofeng Li, Zhongshan Song, Qiankun Hu, Jin Tan, Yuanshun |
| description | This paper addresses the problem of robust stability for quaternion-valued neural networks (QVNNs) with leakage delay, discrete delay and parameter uncertainties. Based on Homeomorphic mapping theorem and Lyapunov theorem, via modulus inequality technique of quaternions, some sufficient conditions on the existence, uniqueness, and global robust stability of the equilibrium point are derived for the delayed QVNNs with parameter uncertainties. Furthermore, as direct applications of these results, several sufficient conditions are obtained for checking the global robust stability of QVNNs without leakage delay as well as complex-valued neural networks (CVNNs) with both leakage and discrete delays. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results. |
| doi_str_mv | 10.1016/j.neunet.2017.04.006 |
| format | Article |
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Based on Homeomorphic mapping theorem and Lyapunov theorem, via modulus inequality technique of quaternions, some sufficient conditions on the existence, uniqueness, and global robust stability of the equilibrium point are derived for the delayed QVNNs with parameter uncertainties. Furthermore, as direct applications of these results, several sufficient conditions are obtained for checking the global robust stability of QVNNs without leakage delay as well as complex-valued neural networks (CVNNs) with both leakage and discrete delays. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.</description><identifier>ISSN: 0893-6080</identifier><identifier>EISSN: 1879-2782</identifier><identifier>DOI: 10.1016/j.neunet.2017.04.006</identifier><identifier>PMID: 28494328</identifier><language>eng</language><publisher>United States: Elsevier Ltd</publisher><subject>Computer Simulation - standards ; Discrete delay ; Global robust stability ; Leakage delay ; Linear matrix inequality ; Modulus inequality technique ; Neural Networks (Computer) ; Quaternion-valued neural networks ; Time Factors ; Uncertainty</subject><ispartof>Neural networks, 2017-07, Vol.91, p.55-65</ispartof><rights>2017</rights><rights>Published by Elsevier Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c362t-1b5c3730e4938cad1133820d1d12c99bbf07380638114bdb4c4edb9ec13790623</citedby><cites>FETCH-LOGICAL-c362t-1b5c3730e4938cad1133820d1d12c99bbf07380638114bdb4c4edb9ec13790623</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.neunet.2017.04.006$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,778,782,3539,27911,27912,45982</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/28494328$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Chen, Xiaofeng</creatorcontrib><creatorcontrib>Li, Zhongshan</creatorcontrib><creatorcontrib>Song, Qiankun</creatorcontrib><creatorcontrib>Hu, Jin</creatorcontrib><creatorcontrib>Tan, Yuanshun</creatorcontrib><title>Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties</title><title>Neural networks</title><addtitle>Neural Netw</addtitle><description>This paper addresses the problem of robust stability for quaternion-valued neural networks (QVNNs) with leakage delay, discrete delay and parameter uncertainties. Based on Homeomorphic mapping theorem and Lyapunov theorem, via modulus inequality technique of quaternions, some sufficient conditions on the existence, uniqueness, and global robust stability of the equilibrium point are derived for the delayed QVNNs with parameter uncertainties. Furthermore, as direct applications of these results, several sufficient conditions are obtained for checking the global robust stability of QVNNs without leakage delay as well as complex-valued neural networks (CVNNs) with both leakage and discrete delays. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.</description><subject>Computer Simulation - standards</subject><subject>Discrete delay</subject><subject>Global robust stability</subject><subject>Leakage delay</subject><subject>Linear matrix inequality</subject><subject>Modulus inequality technique</subject><subject>Neural Networks (Computer)</subject><subject>Quaternion-valued neural networks</subject><subject>Time Factors</subject><subject>Uncertainty</subject><issn>0893-6080</issn><issn>1879-2782</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kE1LXDEUhoNUdLT9ByJZdnOvOUl6b7IRRNoqCIK065CPMzTj_RiTXGX-fTOMdtnVu3ne83IeQi6AtcCgu9q0Ey4TlpYz6FsmW8a6I7IC1euG94p_IiumtGg6ptgpOct5wyqhpDghp1xJLQVXK_L8NLslF5qLdXGIZUftZIddjpnOa_qy2IJpivPUvNphwUDrZrJDjfI2p-dM32L5Q0sckQYc7C7XeqBbm-yItUmXyWMqNk4lYv5Mjtd2yPjlPc_J7x_ff93eNQ-PP-9vbx4aLzpeGnDfvOgFQ6mF8jYACKE4CxCAe62dW7NeKNYJBSBdcNJLDE6jB9Fr1nFxTr4e7m7T_LJgLmaM2eMw2AnnJRtQWgP0vdij8oD6NOeccG22KY427Qwws9dsNuag2ew1GyZNlVhrl-8Lixsx_Ct9eK3A9QHA-udrxGSyj1hlhJjQFxPm-P-Fvx2MkmQ</recordid><startdate>201707</startdate><enddate>201707</enddate><creator>Chen, Xiaofeng</creator><creator>Li, Zhongshan</creator><creator>Song, Qiankun</creator><creator>Hu, Jin</creator><creator>Tan, Yuanshun</creator><general>Elsevier Ltd</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>201707</creationdate><title>Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties</title><author>Chen, Xiaofeng ; Li, Zhongshan ; Song, Qiankun ; Hu, Jin ; Tan, Yuanshun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-1b5c3730e4938cad1133820d1d12c99bbf07380638114bdb4c4edb9ec13790623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Computer Simulation - standards</topic><topic>Discrete delay</topic><topic>Global robust stability</topic><topic>Leakage delay</topic><topic>Linear matrix inequality</topic><topic>Modulus inequality technique</topic><topic>Neural Networks (Computer)</topic><topic>Quaternion-valued neural networks</topic><topic>Time Factors</topic><topic>Uncertainty</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Xiaofeng</creatorcontrib><creatorcontrib>Li, Zhongshan</creatorcontrib><creatorcontrib>Song, Qiankun</creatorcontrib><creatorcontrib>Hu, Jin</creatorcontrib><creatorcontrib>Tan, Yuanshun</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Neural networks</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Xiaofeng</au><au>Li, Zhongshan</au><au>Song, Qiankun</au><au>Hu, Jin</au><au>Tan, Yuanshun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties</atitle><jtitle>Neural networks</jtitle><addtitle>Neural Netw</addtitle><date>2017-07</date><risdate>2017</risdate><volume>91</volume><spage>55</spage><epage>65</epage><pages>55-65</pages><issn>0893-6080</issn><eissn>1879-2782</eissn><abstract>This paper addresses the problem of robust stability for quaternion-valued neural networks (QVNNs) with leakage delay, discrete delay and parameter uncertainties. 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| ispartof | Neural networks, 2017-07, Vol.91, p.55-65 |
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| source | MEDLINE; ScienceDirect Journals (5 years ago - present) |
| subjects | Computer Simulation - standards Discrete delay Global robust stability Leakage delay Linear matrix inequality Modulus inequality technique Neural Networks (Computer) Quaternion-valued neural networks Time Factors Uncertainty |
| title | Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties |
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